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There are several reasons that make it desirable to improve mathematical tools used in the nonlocal theory of highly singular quantum fields with an exponential or faster high-energy behaviour. First of all string theory gives us new indications [1-3] that the concept of space-time manifold is only approximate and valid at length scales coarser than the Planck scale. Certainly, one or another kind of nonlocality arises at any attempt to unify quantum gravity with other fundamental interactions, however it is of great interest that just the exponential growth is characteristic of the spectral densities which occur in the Källen-Lehmann representations for string propagators with pointlike boundary conditions [4,5]. A second reason concerns the problem of formulating causality which is crucial for any nonlocal theory. Recall that the exponential bound on the off-mass-shell amplitudes has been found by Meiman [6] just from the microcausality considerations. For faster momentum-space growth, no definite criterion of macrocausality in terms of observables has been obtained as yet. However a mathematical analog of local commutativity has been found which ensures a number of important physical consequences for arbitrary high-energy behaviour. These include the existence of the unitary scattering matrix [7] and the polynomial boundedness of the scattering amplitudes within the physical region of variables [8,9]. It is surprising enough that the connection between spin and statistics and the $TCP$-invariance derived previously [10-12] for quasilocal fields can also be established [13-15] in the essentially nonlocalizable case when the holomorphy domain of vacuum expectation values becomes empty and radically new proofs are needed. Thirdly, the use of highly singular nonlocal form-factors [16] turns out to be effective for a phonomenological description of strong interactions [17-18]. | 1,907 | hep-th/9211099 | 36,668 | 1,992 | 11 | 24 | false | true | 1 | UNITS |
This does not yet look like the functional Schroedinger equation for the scalar field. However, we may recall that formally the expression inside the square root is divergent. However, it may not be actually divergent because in computing (66) we have assumed that the scalar field is slowly varying on the scale of the weave. If we investigate the action of (65) on states which have support on $\phi (x)$ that are fluctuating on the Planck scale, we can see that in the limit that the regulator is removed the effect of the $T^{ab}$'s is to insure that the the terms in $(\partial_a\phi)^2$ only act at those points which are on the lines of the weave. That is, in the limit of small distances we have a description of a scalar field propagating on a one dimensional subspace of $\Sigma$ picked out by the weave. That is, on scales much smaller than the Planck scale the scalar field is propagating as a $1+1$ dimensional scalar field. | 937 | gr-qc/9301016 | 44,883 | 1,993 | 1 | 15 | false | true | 2 | UNITS, UNITS |
These results make possible the construction of a correspondence between any three geometry whose curvature is small in Planck units and a diffeomorphism invariant state of the gravitational and matter fields. This correspondence relies on the approximation of the classical geometry by a piecewise flat Regge manifold, which is then put in correspondence with a diffeomorphism invariant state of the gravity-matter system in which the matter fields specify the faces of the triangulation and the gravitational field is in an eigenstate of the operators that measure their areas. ${}^*$ [email protected] | 611 | gr-qc/9302011 | 49,758 | 1,993 | 2 | 10 | false | true | 1 | UNITS |
For polynomial actions a lot of attention has been given to the existence of a pseudo Fokker-Planck (F-P) equation which describes the dynamics of a possibly equivalent complex valued weight function [CIT]. In earlier investigations especially the spectrum of this operator played a major role [CIT]. But statements on the properties of the spectrum are not sufficient to draw conclusions on the correctness or the convergence of CL [CIT]. Certainly, if one can show that the pseudo F-P equation exists and that the real part of the spectrum of the operator is semidefinite then CL converges but not necessarily to the desired result. Further conditions must hold (see [CIT]). Except for very simple cases it is hard and most unlikely to get exact information on the complete spectrum. Certainly there always exist the real F-P operator for the process and the convergence of the process follows if one can prove that the operator has a unique nonnegative integrable solution to the zero eigenvalue. But this is also very hard and so far there is no classification scheme for actions which have the suitable properties. So, to get information on the convergence for any problem one must check either the existence and the whole spectrum of the pseudo F-P operator or the zero eigenvalue properties of the real F-P operator. In practice therefore the question of convergence still remains a matter of experiment and experience. | 1,426 | hep-lat/9312003 | 121,625 | 1,993 | 12 | 1 | false | true | 1 | FOKKER |
What are the exact conditions under which the semiclassical Hamilton-Jacobi equation is valid? The first, obvious, condition is that the expectation value of ${\cal H}$ with respect to the state satisfying the approximate Schrödinger equation be *small* compared to the other terms in (4.15). This came out in a natural way through the expansion scheme with respect to the Planck mass. The second condition, as has been discussed in section 4.1, is the smallness of interference terms between different WKB components of the total state. This is the analogy of the smallness of interferences between the different components of (2.6) and is a necessary condition for the validity of a Born-Oppenheimer approximation. As shown in section 4.1, these various components decohere in realistic cases and thereby justify the use of a single WKB component. | 849 | gr-qc/9312015 | 124,109 | 1,993 | 12 | 9 | true | true | 1 | UNITS |
In this newly defined notation, the overdamping constraint is written as FORMULA and the density perturbation constraint is FORMULA Using the equation of motion [1.8] and the relation FORMULA we can write the condition that the universe is dominated by potential energy rather than kinetic energy (Eq. [1.10]) in the form FORMULA where ${M_{\rm pl}}$ is the Planck mass. Furthermore, the quantities $\Delta V$ and $\Delta \phi$ can be written in the form FORMULA FORMULA We have chosen our sign convention so that $\Delta V$ is a positive quantity and so that $x=0$ at the beginning of the constrained time period. Keep in mind that $\Delta V$ and $\Delta \phi$ are the changes in the potential and the inflation field during the $N=8$ e-foldings during which cosmic structure is produced; they are *not* the total changes in these quantities over the entire inflationary epoch. | 878 | astro-ph/9401006 | 131,650 | 1,994 | 1 | 7 | true | false | 1 | UNITS |
In Section REF we describe the stochastic inflation formalism [CIT] for Jordan--Brans--Dicke inflation, see also [CIT]. The Brownian motion of the scalar fields in de Sitter space can be written as a Langevin equation for the coarse-grained fields with an effective white noise generated by quantum fluctuations. The associated Fokker--Planck equation for the probability distribution of finding a given value of the scalar fields in a given point of space-time can be derived from the Langevin equation and written in a form which is manifestly time-reparametrization invariant. The proper way to find stationary solutions is to solve the diffusion equation subject to certain well defined boundary conditions [CIT]. We show that the probability distribution far from the Planck boundary behaves like a Gaussian with fields centered at their classical trajectories and we calculate its dispersion coefficients. The probability distribution in the physical frame takes into account the exponential growth of each inflationary domain. The condition for self-reproduction of the universe is then calculated. Those inflationary domains with fields inside the region of self-reproduction will dominate the proper volume of the universe and will tend to diffuse towards the Planck boundary. | 1,285 | astro-ph/9401042 | 136,744 | 1,994 | 1 | 24 | true | true | 3 | FOKKER, FOKKER, FOKKER |
Chaotic inflation scenario [CIT] has brought two surprises. First of all, it was realized that inflation can occur even if there was no thermal equilibrium in the early Universe, and even if the effective potential $V(\phi)$ does not have any maximum at all, or if its maximum is not sufficiently flat. In particular, chaotic inflation scenario can be realized in the theories with potentials ${m^2\over 2} \phi^2$, ${\lambda\over 4} \phi^4$, ${\lambda\over 4} ({\phi^2 - {m^2\over \lambda}})^2$, and $e^{\alpha\phi}$. But the most surprising realization was that inflation in these theories also goes on without end. Due to quantum fluctuations the scalar field $\phi$ in some parts of the Universe perpetually climbs to higher and higher values of its potential energy $V(\phi)$, until it approaches the Planck density $M_P^4$. The existence of this regime may seem counterintuitive. Indeed, the probability that the field jumps up all the time is very small. However, those rare domains where it happens continue growing exponentially, much faster than the domains with small $V(\phi)$. This scenario was called "eternal inflation" [CIT]. | 1,143 | hep-th/9402115 | 145,134 | 1,994 | 2 | 20 | true | true | 1 | UNITS |
Due to the existence of a minimum proper interval, the notion of event loses one of its characteristic features: it is no longer an invariant concept [CIT]. The uncertainty in the radius of the black hole horizon may be interpreted as giving rise to a membrane, a stretched horizon, from the point of view of an observer at rest with respect to the black hole (for a study of the effect of a Planck's length cutoff on black-hole evaporation, see also Ref. [CIT]). However, this membrane would be real only for this observer at rest (its reality would be dramatically shown if this observer were too close to the membrane since its extremely high temperature would burn him to ashes). A free-falling observer would not see or feel this membrane since, for him, nothing special would take place at the horizon; in fact, there would be no horizon for him. The absolutely different perceptions of both observers can be stated [CIT] (see also Refs. [CIT] for related ideas) in terms of a black hole complementarity principle: events are observer-dependent, in the same manner as in quantum mechanics the answer to the question "Is an electron particlelike or wavelike?" depends on the kind of measure that is performed, or as in special relativity the issue of simultaneity of two events depends on the observer. The physical laws appear the same in all reference systems but the description of the physical reality may vary from observer to observer. | 1,446 | gr-qc/9403008 | 147,485 | 1,994 | 3 | 2 | false | true | 1 | UNITS |
In addition, we should not forget that the fermion masses are much closer to the weak scale, rather than the Planck scale, so it does not seem to us too unnatural trying to explain them in terms of physics coming in at the weak scale, rather than expecting "Planck-\" or higher-scale physics to "feed down\" their effect directly to the fermion masses. Of course, the weak scale itself could still be determined by some unknown high-energy physics, appearing at the "Planck\", or even at the highest ETC, scale. Therefore, the proposed mechanism, when seen from this point of view, does not completely violate the way high-energy physics determine low-energy physics. It just gives the weak scale a more active and direct role in the fermion mass generation, while leaving for the Planck-scale, or for any other scale that determines the weak scale, only an indirect role. | 872 | hep-ph/9403220 | 147,968 | 1,994 | 3 | 3 | false | true | 4 | UNITS, UNITS, UNITS, UNITS |
Inspired by the work of Wheeler among others, we have studied the problem of quantum measurements of space-time distances by applying the general principles of quantum mechanics as well as those of general relativity. Contrary to the folklore, the minimum error in the measurement of a length is shown to be proportional to the one-third power of the length itself. This uncertainty in space-time measurements implies an uncertainty of the space-time metric and yields quantum decoherence for particles heavier than the Planck mass. There is also a corresponding minimum error in energy-momentum measurements. | 609 | hep-th/9406110 | 182,853 | 1,994 | 6 | 16 | false | true | 1 | UNITS |
Apart from the general laws of motion, one requires a set of initial conditions for the universe. Early models of inflation postponed the issue by assuming that the universe started in a very hot state that supercooled in a metastable vacuum, which then decayed to the true vacuum [CIT]. But in fact, the only reasonable approach to the initial value problem is the use of quantum cosmology since the most natural initial conditions for inflation are at Planck scale, where quantum fluctuations of the space-time metric become important. This was particularly emphasized in the chaotic inflation scenario [CIT], which opened the possibility of arbitrary initial conditions for the inflaton field in arbitrary effective potentials. A question remained, what is the probability distribution for those inflationary domains that started their evolution close to the Planck boundary? Quantum cosmology proposed an answer, based on the path integral formulation of quantum gravity, which is still under debate [CIT]. In the meanwhile, the so called stochastic approach to inflation was developed [CIT]. This formalism takes into account the Brownian motion of the inflaton field under the effect of its own quantum fluctuations and is described with the help of ordinary diffusion equations. | 1,285 | astro-ph/9407087 | 197,391 | 1,994 | 7 | 27 | true | true | 2 | UNITS, UNITS |
On the basis of our experience with a wide class of potentials (we have found similar effects for the quadratic and quartic potentials of chaotic inflation) we want to conclude that the presence of quantum inflation seems to be a generic feature of field theoretical models addressing Planck scale physics and it may be interesting and fruitful to explore this phenomenon in more detail. | 387 | hep-ph/9408267 | 202,113 | 1,994 | 8 | 10 | false | true | 1 | UNITS |
Expression (33) means that quantum corrections result in the shifting the horizon radius by the Planck distance. For the charged black hole with $Q<M<\sqrt{\frac{25}{24}}Q$ the quantum corrections decrease the horizon radius while for $M>\sqrt{\frac{25}{24}}Q$ it is increasing. The quantum corrected entropy is determined then with respect to this quantum corrected horizon in such a way that the law (1) remains valid. For massive black hole ($M>>M_{pl}$) this shifting of horizon is negligible. However, it becomes essential and important for black hole of the Planck mass. | 576 | hep-th/9408068 | 202,792 | 1,994 | 8 | 12 | false | true | 2 | UNITS, UNITS |
This is the second part of a binary paper discussing Fokker-Planck models matched with observations of the globular cluster NGC 6397. In the first paper (Drukier 1994; Paper A), the details of the modeling and comparison techniques were discussed, as was an overview of results of the over 1000 models run. Briefly, the models solve the isotropic, orbit-averaged form of the Fokker-Planck equation, where the distribution functions are functions of energy and mass. An energy source in the form of a statistical treatment of binaries formed in three-body reactions is used to reverse core collapse. The models also include a tidal boundary and the effects of mass-loss due to stellar evolution. More details are given in Paper A together with definitions for many of the symbols used here. The data used for the comparisons are the surface density profile (SDP) and two mass functions (MFs) from, the intermediate-distance mass-function from and the velocity dispersion profile from. Again, I follow the naming convention of and refer to the three mass functions as the du Pont:if, FRST, and du Pont:out MFs in order of distance from the cluster center. | 1,153 | astro-ph/9409087 | 217,897 | 1,994 | 9 | 29 | true | false | 2 | FOKKER, FOKKER |
Another possibility is that the Universe was large and hot from the very beginning, and it became inflationary only when its thermal energy density $\sim T^4$ dropped below $V(\phi)$. Inflation begins at this stage only if the Universe at this moment was sufficiently homogeneous on a scale greater than $\Delta x \sim H^{-1} \sim 1/\sqrt{V(\phi)}$. Suppose for simplicity that the Universe from the very beginning was dominated by ultrarelativistic matter. Then its scale factor expanded as $\rho^{-4}$, where $\rho$ is the energy density at the pre-inflationary stage. Therefore at the Planck time the size of the part of the Universe which later evolved into inflationary domain was not $1/\sqrt{V(\phi)}$, but somewhat smaller: $\Delta x \sim V^{-1/4}(\phi)$. This whole scenario can work only if at the Planck time the domain of this size was sufficiently homogeneous, ${\delta \rho \over \rho} \ll 1$. However, at the Planck time this domain consisted of $V^{-3/4}(\phi)$ domains of a Planck size, and energy density in each of them was absolutely uncorrelated with the energy density in other domains. Therefore *a priori* one could expect changes of density $\delta \rho \sim \rho$ when going from one causally disconnected parts of the Universe of a size $M_P^{-1} = 1$ to another. Simple combinatorial analysis suggests that the probability of formation of a reasonably homogeneous part of the Universe of a size $\Delta x \sim V^{-1/4}(\phi)$ at the Planck time is suppressed by the exponential factor FORMULA where $C = O(1)$. To get a numerical estimate, one can take $V(0) \sim 10^{-10}$. This gives $P { \lower-1.2pt\vbox{\hbox{\rlap{$<$}\lower5pt\vbox{\hbox{$\sim$}}}} } 10^{-10^{7}}$. | 1,701 | hep-th/9410082 | 222,706 | 1,994 | 10 | 12 | true | true | 5 | UNITS, UNITS, UNITS, UNITS, UNITS |
The superstring dilaton also demonstrates this property of dynamical Planck fields. A kinetic inflation from the dilaton of superstring theories was discussed independently in Refs. [CIT]. Recently, there have been interesting studies of an inflating superstring cosmology in higher dimensions (see for example [CIT]). In those papers it is the dilaton which drives the inflation. The extra dimensions exist only as a consequence of the nature of string theory. By contrast, in this paper it is the extra dimensions themselves which drive the inflation. As will be discussed, the extra dimensions act very much like the superstring dilaton. | 640 | gr-qc/9411041 | 235,570 | 1,994 | 11 | 15 | true | false | 1 | OTHER |
On more phenomenological grounds, there is also a problem of scales which requires further studies. The scalar field which is part of the Riemann connection and is related to the distance between the two sheets of space--time, pertaining to the intrinsic structure of the latter, has as a natural scale, the Planck length. On the other side, according to the Connes and Lott model [CIT], at low energy this distance must be the inverse of the top quark mass, which is several order of magnitude larger than the Planck length, to correctly reproduce the electroweak standard model. We would like to stress that an important feature of our work is to look at the distance as undergoing a dynamical evolution. It remains a challenging programme to study the dynamics responsible for the subsequent evolution of the distance down to the electroweak scale. | 851 | gr-qc/9503040 | 285,636 | 1,995 | 3 | 22 | false | true | 2 | UNITS, UNITS |
A reason to consider finite temperature quantum field theories is mainly based on the recent developments of cosmological models. According to the standard Big-Bang cosmology and the more recent inflationary models, the very early universe has passed through a phase of thermal equilibrium at very high temperature and density, where the symmetry was restored but with a large cosmological constant. As the universe has become cool, it has gone through several phase transitions (see for example Ref. [CIT]). Although the usual thermodynamical concepts may be inappropriate in the presence of very strong gravitational interactions, the need for considering finite temperature field theory in a curved background has been arisen. Strictly speaking, it has been shown that thermal equilibrium can be maintained for conformally invariant field theories in conformally flat expanding space-times [CIT]. Otherwise the expansion must be nearly adiabatic [CIT]. On the other hand, particle production in a hot Friedman universe is exponentially suppressed due to the increase of the mass by thermal effects at temperatures smaller than the Planck one [CIT] and the expansion should be nearly adiabatic. Phase transitions in de Sitter space-time have been first considered in Ref. [CIT] with the important result that critical behaviour strongly depends on curvature. Very little is known about them in anti-de Sitter space-time, mainly because de Sitter is more relevant than anti-de Sitter in inflationary scenarios. | 1,511 | hep-th/9505061 | 306,358 | 1,995 | 5 | 10 | false | true | 1 | UNITS |
Here we point out that the time evolution in 4D quantum gravity is described by a Langevin equation for 3-geometries in terms of the Ashtekar's canonical field variables by showing that the corresponding Fokker-Planck hamiltonian operator exactly recovers the hamiltonian of 4D Euclidean quantum gravity in the gauge $N=1$ and $N^i = 0$[^4]. The Hartle-Hawking type boundary condition is naturally imposed in this scheme by specifying the initial probability distribution functional. We also present the lattice regularization of this approach which defines a lattice regularization of Ashetekar's canonical formalism [CIT]. | 624 | hep-th/9509087 | 362,126 | 1,995 | 9 | 18 | false | true | 1 | FOKKER |
We consider a 2-parameter class of solvable closed superstring models which `interpolate' between Kaluza-Klein and dilatonic Melvin magnetic flux tube backgrounds. The spectrum of string states has similarities with Landau spectrum for a charged particle in a uniform magnetic field. The presence of spin-dependent `gyromagnetic' interaction implies breaking of supersymmetry and possible existence (for certain values of magnetic parameters) of tachyonic instabilities. We study in detail the simplest example of the Kaluza-Klein Melvin model describing a superstring moving in flat but non-trivial 10-d space containing a 3-d factor which is a `twisted' product of a 2-plane and an internal circle. We also discuss the compact version of this model constructed by `twisting' the product of the two groups in SU(2) x U(1) WZNW theory without changing the local geometry (and thus the central charge). We explain how the supersymmetry is broken by continuous `magnetic' twist parameters and comment on possible implications for internal space compactification models. (Contribution to the Proceedings of the 1995 Erice School "String Gravity and Physics at the Planck Scale") | 1,175 | hep-th/9510041 | 370,965 | 1,995 | 10 | 7 | false | true | 1 | UNITS |
This model contains a similar structure to the "hybrid\" inflation models, proposed by Linde and studied by Copeland, Liddle, Lyth, Stewart, and Wands [CIT]. The fact that the standard dimensional naturalness arguments for the number of $e$-foldings and for $\delta \rho/\rho$ do not apply, and that the Hubble scale during inflation will be low was also clearly recognized by these authors. Our point here is to emphasize that the most natural scales for successful implementation of two field inflation of the "waterfall\" type are the scales associated with supersymmetry breaking and the Planck scale. Furthermore, our models more accurately reflect masses and couplings associated with flat direction fields, and we will motivate the parameters and potential we use by consideration of flat directions in the MSSM. Hybrid inflation in the context of SUSY leads one to the interesting conclusion that the Hubble scale during the inflation which established the density perturbations might have been of order $10^3$--$10^4$ GeV, rather than $10^{13}$ GeV. | 1,058 | hep-ph/9601296 | 419,337 | 1,996 | 1 | 18 | true | true | 1 | UNITS |
We have shown that with more than one field it is possible to construct models of inflation with no small parameters. Furthermore, the mass scales which seem to most naturally appear in these models are of order $m_{3/2}$, about 1 TeV, and $M_I$, about $10^{11}$ GeV, leading to a natural association with supersymmetric models. These models give rise to the correctly normalized density perturbations, even though the Hubble constant is quite low, of order $10^3-10^4$ GeV, because the value of the inflaton field at the end of inflation is much lower than the Planck scale. The key to producing more such models is a sensitive dependence of the $\phi$ potential on the value of the $\psi$ field, so that the motion of the $\psi$ field can trigger the end of inflation while its value is small. | 795 | hep-ph/9601296 | 419,367 | 1,996 | 1 | 18 | true | true | 1 | UNITS |
Supersymmetry is an elegant extension of the standard model of particle physics. It is the only so-far "unused" symmetry of the Poincare group and has the virtue of protecting the weak scale against radiative corrections from GUT and Planck scale. Local supersymmetry appears to be an attractive route towards unifying all four forces and is a basic ingredient in superstring theory. Supersymmetry transforms bosons into fermions (and vice-versa). As supersymmetry has a new symmetry, R parity, it can imply the existence of a new stable particle. In much of the parameter space of the minimal supersymmetric model, this new stable particle (which we will refer to as the"neutralino") has predicted properties such that it would comprise much of the density of the universe [CIT]. | 780 | astro-ph/9603026 | 443,388 | 1,996 | 3 | 6 | true | false | 1 | UNITS |
Now in the gauged NJL model, QCD plus four-fermion interaction (REF), essentially the same mechanism as the above is operative. Based on the very slowly damping solution of the ladder SD equation (REF) and the PS formulas, (REF) and (REF), MTY [CIT] predicted $m_t$ and $\delta \rho$ as the *decreasing function of cutoff $\Lambda$*. For the Planck scale cutoff $\Lambda\simeq 10^{19} \hbox{GeV}$, we have: [CIT] [^5] | 417 | hep-ph/9603277 | 446,175 | 1,996 | 3 | 12 | false | true | 1 | UNITS |
We also consider the particular initial conditions problem faced by a spatially closed FRW universe, which in the absence of fine-tuning will typically have a lifetime on the order of the Planck scale [CIT]. This problem persists in the presence of inflation: although inflation can begin at the Planck scale there is no guarantee that it will do so. Here we show that the contribution from the one-loop terms can allow a closed universe to grow arbitrarily large, ensuring that the universe will survive long enough for inflation to begin. | 540 | hep-th/9605173 | 487,880 | 1,996 | 5 | 23 | true | true | 2 | UNITS, UNITS |
Notice that postulate 1 already adds the Planck's constant to classical physics. Consider a classical system described by a variable $q$ that takes bounded but continuous values; for instance, the position of a particle. Classically, the amount of information we can gather about it is infinite: we can locate its state in the system's phase space with arbitrary precision. Quantum mechanically, this infinite localization is impossible because of postulate 1. Thus, maximum available information can localize the state only within a finite region of the phase space. Since the dimensions of the classical phase space of any system are $(L^{2}T^{-1}M)^n$, there must be a universal constant with dimension $L^{2}T^{-1}M$, that determines the minimal localizability of objects in phase space. This constant is of course Planck's constant. Thus we can view Planck's constant just as the transformation coefficient between physical units (position $\times$ momentum) and information theoretical units (bits). | 1,005 | quant-ph/9609002 | 550,042 | 1,996 | 8 | 31 | false | true | 3 | CONSTANT, CONSTANT, CONSTANT |
Regardless of the relative sizes of $G$ and $l$, the entropy is always minimized for $A_+ \leq G$. If we assume $G<<l$ then (REF) is solved as $A_{+min}={2\over 3}G$, However if $G >> l$, then (REF) becomes (for $\mu=0$, say) $A_+/G \simeq e^{-A_+/l} < 1$. In either case, the minimum of the entropy occurs for a hole whose horizon area is of the order of the Planck length $r_{+}\sim l_{pl}$. In the process of evaporation the horizon area of a hole typically shrinks. The evaporation is expected to stop when the black hole takes the minimum entropy configuration. In our case it is the configuration with horizon area $A_+=A_{+ min}$. Presumably it has zero temperature and its geometry is a reminscent of an extremal black hole. However at present we cannot definitively conclude this since our considerations do not take into account quantum back reaction effects. These effects are supposed to drastically change the geometry at a distance $r\sim l_{pl}$. Therefore the minimum entropy configuration is likely to have little in common with the classical black hole configuration described in Section 2. Further investigation of this issue will necessitate taking the back reaction into account. | 1,200 | hep-th/9609085 | 555,824 | 1,996 | 9 | 10 | false | true | 1 | UNITS |
We gratefully acknowledge many fruitful interactions with Marcela Carena, Mariano Quiros, and Carlos Wagner. We also appreciate useful conversations with Damien Pierce and Fabio Zwirner. Two of us (HEH and RH) would like to thank the Institute for Theoretical Physics in Santa Barbara for their partial support under the National Science Foundation Grant No. PHY94-07194 during the final phase of this project. One of us (HEH) is grateful for the hospitality of the Institut für Theoretische Teilchenphysik in Karlsruhe and the Max-Planck-Institut für Physik in Munich, where some of this work was accomplished. HEH is supported in part by the U.S. Department of Energy, and AHH is supported by the Graduiertenkolleg *Elementarteilchenphysik*, Karlsruhe. | 754 | hep-ph/9609331 | 557,235 | 1,996 | 9 | 12 | false | true | 1 | MPS |
Since the metric (REF) is a one-loop approximation, it is valid only in the region where $R l{}_{P}{}^{2} < 1$ (since the loop-expansion of the effective metric is in $\left\langle T{}^{n}\right\rangle$, which is of the order of $(Rl{}_{P}{}^{2}){}^{n}$). This gives that $r_{AH} > {\sqrt 2}l_P$, which is the expected Planck length cutoff. Note that if one defines a dynamical black hole mass $M_E$ as $M_E = {1\over2}r_{AH}$, then FORMULA which does not correspond to a thermal evaporation mass equation which is given by ${dM_E\over dv}\propto - M_{E}^{-2}$. However, because $\beta$ is very small (in physical units it is given by $\beta = {N\over 384\pi}(m_P / M){}^{2}$ where $m_P$ is the Planck mass), the difference between the non-thermal evaporation (REF) and a thermal one will be noticed only when $r_{AH} < r_c \approx \frac45 r_s$. Therefore the evaporation is thermal for $r_{AH} > r_c >> l_P$. | 909 | hep-th/9611219 | 607,063 | 1,996 | 11 | 26 | false | true | 2 | UNITS, UNITS |
The pattern of variations in the intensity of magnetodipole losses is studied with the relativistic effect of magnetic-field dissipation during collapse into a black hole taken into account. A burst-type solution can be obtained both for a direct collapse and for the formation of a rapidly-rotating, self-gravitating object - a spinar - using a simple model. Analytical dependences on radius describing an electromagnetic burst are derived. The time dependence of the burst shape for an infinitely distant observer and the maximum energy of relativistic particles accelerated by an electric field are numerically calculated. The objects under consideration are of particular interest because particles in their vicinity can be accelerated up to the Planck energies. Possible astrophysical applications to the theory of active galactic nuclei (AGNs) and QSOs are briefly discussed. It is shown for the first time that a spinar can be produced by a merger of neutron stars; this possibility is considered in and without connection with the formation of gamma-ray bursts. | 1,069 | astro-ph/9703006 | 664,920 | 1,997 | 3 | 1 | true | false | 1 | UNITS |
3. **Nearly scale-invariant spectrum of gravitational waves.** These gravitational waves have wavelengths from ${\cal O}(1\rm,km)$ to the size of the present Hubble radius and beyond. Described in terms of a power spectrum for the dimensionless gravity-wave amplitude at early times, $P_T(k) \equiv \langle |h_k|^2 \rangle = A_Tk^{n_T-3}$, where the spectral index $n_T \approx 0$ (the scale-invariant limit is $n_T =0$). As before, the power spectrum specifies the variance of the Fourier components. Once again, the overall amplitude $A_T$ is model dependent (varying as the value of the inflationary vacuum energy). Unlike density perturbations, which are required to initiate structure formation, there is no cosmological lower bound to the amplitude of the gravity-wave perturbations. Tensor perturbations also give rise to CBR anisotropy; requiring that they do not lead to excessive anisotropy implies that the energy density that drove inflation must be less than about $(10^{16},{\rm GeV})^4$. This indicates that if inflation took place, it did so at an energy well below the Planck scale.[^7] | 1,103 | astro-ph/9703196 | 681,523 | 1,997 | 3 | 31 | true | true | 1 | UNITS |
The link between black holes and Planck scale phenomena was already suggested in paperI, and it has been investigated here how very small and very large scale physics are linked. The existence of a charge threshold at which the QGUT symmetry is broken, is equivalent to a quiescent and stable quantum foam which derives from a relatively small set of macroscopic black holes. *This macroscopic set of black holes, as a measure of the topology of the universe, fixes the Planck scale quantum fluctuations, and the nature of field interactions*. | 543 | gr-qc/9704036 | 691,576 | 1,997 | 4 | 14 | false | true | 2 | UNITS, UNITS |
Our present view of things is quite different. The renormalization group philosophy can be applied to the standard model itself. Imagine that we have a unified theory whose characteristic energy scale, $\Lambda$, is very large or whose characteristic distance scale, $\hbar c /\Lambda$, is very small (say the Planck length of $10^{ 33}$cm.). Assume further that just below this scale the theory can be expressed in terms of local field variables. As to what happens at the unification scale itself we assume nothing, except that just below this scale the theory can be described by a local quantum field theory. (String theory does provide us with an example of such a unified theory, which includes gravity and can be expressed by local field theory at distances much larger than the Planck length.) Even in the absence of knowledge regarding the unified theory, we can determine the most general quantum field theory. In absence of knowledge as to the principles of unification this theory has an infinite number of arbitrary parameters describing all possible fields and all possible interactions. We also assume that all the dimensionless couplings that characterize the theory at energy $\Lambda$ are of order one (what else could they be?). Such a theory is useless to describe the physics at high energy, however, at low energies, of order $E$, the effective dynamics, the effective Lagrangian that describes physics up to corrections of order ${E/\Lambda }$, will be parameterized by a finite number of couplings. The renormalization group describes how the various couplings run with energy. We start at $\Lambda$ with whatever the final unified theory and then one can show that the low energy physics will be described by the most general renormalizable field theory consistent with the assumed couplings plus non-renormalizable interactions that are suppressed by powers of the energy relative to the cutoff. If we demand further that the theory at the scale $\Lambda$ contain the local gauge symmetry that we observe in nature, then the effective low energy theory will be described by the standard model up to terms that are negligible by inverse powers of the large scale compared to the energy that we observe. The extra interactions will give rise to weak effects, such as gravity or baryon decay. But these are very small and unobservable at low energy. | 2,372 | hep-th/9704139 | 695,388 | 1,997 | 4 | 18 | false | true | 2 | UNITS, UNITS |
In keeping with the analysis of the previous section we discuss thermalization induced by synchrotron self--absorption using the Fokker--Planck equation. Instead of attempting to solve the complete integrodifferential equation (eq. [REF]), we check for consistency by assuming that the (thermal) synchrotron radiation is highly self--absorbed, and then determining whether the thermalization timescales obtained from the Fokker--Planck coefficients are faster than the accretion time. | 484 | astro-ph/9705067 | 708,557 | 1,997 | 5 | 9 | true | false | 2 | FOKKER, FOKKER |
An adjoint alone is not sufficient to break $SO(10)$ to the Standard Model group, $G_{SM}$, and in particular cannot reduce the rank of the group. This requires either spinorial Higgs (${\bf 16} + \overline{{\bf 16}}$) or rank-five antisymmetric tensor Higgs (${\bf 126} + \overline{{\bf 126}}$). As the latter tend to destroy the perturbativity of the unified interactions below the Planck scale, we will assume that the rank-breaking sector has spinors, which we shall call $C$ and $\overline{C}$. These spinors (also necessary to give mass to the right-handed neutrinos) have VEVs in the $SU(5)$-singlet direction. | 617 | hep-ph/9705366 | 716,045 | 1,997 | 5 | 20 | false | true | 1 | UNITS |
Now under the above strong energy condition we shall prove the relation as FORMULA where $t$ may be taken to be any time between the Planck time and the decoupling time. We take the standpoint that the matter content of the Universe is well understood after the big bang nucleosynthesis. In order to evaluate the integral in Eq.(REF), we divide the time range into two epochs: (1) from the Planck time $t_{pl}$ to the time of nucleosynthesis $t_{nuc}$ which is defined by the time when the neutron-to-proton ratio is frozen out; (2) from $t_{nuc}$ to the time of the decoupling of the microwave background $t_{dec}$. In epoch (1), we assume that matter obeys the energy condition such that FORMULA which has been derived under the strong energy condition with positive energy density. In epoch (2), the universe is dominated by the ordinary dust matter and radiation. | 867 | gr-qc/9707043 | 765,316 | 1,997 | 7 | 18 | true | false | 2 | UNITS, UNITS |
Finally, as easily seen from the Table (REF) that all interesting effects of the d-term are proportional to the value of ${\delta_{GS}}$ hence quickly become unimportant when the mass scale of the F-I parameter becomes smaller than $M_{planck}$. Also, after supersymmetry breaking induced by some third party one can have induced d-terms with F-I effective parameters $\xi \sim m^2_{3/2} \log m^2_{3/2}$ which for reasonable values of $m^2_{3/2} \sim 1 TeV^2$ gives $\frac{\xi}{M^2} \leq 10^{-30}$ resizing all the interesting features discussed above down to nothing. | 568 | hep-ph/9708410 | 789,880 | 1,997 | 8 | 20 | false | true | 1 | UNITS |
Concerning the unification of the gauge couplings, string theory is more powerful than field theory because now also gravity is fully unified with the gauge interactions. In particular, in the heterotic string at tree level at the unification scale one finds [CIT] a relation between the Newton's constant $G_N$, the string coupling constant $g_s$ and the gauge coupling constants of the various gauge groups $g_i$'s given by: FORMULA where the constants $k_i$ are the central charges of the Kac-Moody algebras. When one takes into account the one loop corrections one can see that the gauge coupling constants will run according to the renormalization group and the scale of the grand unification can be computed in terms of the string coupling constant and the Planck mass obtaining [CIT] ($\gamma$ is the Euler-Mascheroni constant): FORMULA But, since $g_s \sim 1$, as follows from the second equation in eq. (REF) where $g_s$ must be identified with $g_{GUT}$, one gets a discrepancy of a factor $20 \sim 30$ between eq. (REF) and the first equation in eq. (REF). This discrepancy is independent on the specific compactification of the six extra dimensions and goes under the name of the string gauge coupling unification problem. In conclusion, although one apriori could have expected that the unification scale of the gauge and gravitational interactions should have been of the order of the Planck mass, it turns out that such a scale is clearly smaller than $M_P$ as follows from eq. (REF), but, however, still a factor $20 \sim 30$ too high in comparison with the extrapolation from the low energy experiments. The various possible resolutions of this problem are reviewed in Ref. [CIT]. | 1,697 | hep-th/9708105 | 790,029 | 1,997 | 8 | 20 | false | true | 2 | UNITS, UNITS |
For the case when one adds the most general Planck scale interaction one finds that fixing the textures in the Higgs doublet sector does not uniquely fix the textures in the Higgs triplet sector [CIT]. One needs a dynamical principle to do so. One possibility suggested is to extend supergravity models to include not only the usual visible and hidden sectors, but also an exotic sector [CIT]. The exotic sector contains new fields which transform non-trivially under the GUT group and couple to the fields in the hidden sector and the adjoint scalars in the visible sector. After spontaneous supersymmetry breaking the exotic fields develop Planck scale masses because of their couplings with the hidden sector fields and integration over the exotic fields leads to the desired Planck scale corrections. For the choice of a minimal set of exotic fields one finds that the Planck scale corrections are uniquely determined and one finds that correspondingly the textures in the Higgs triplet sector are uniquely determined. | 1,022 | hep-ph/9708469 | 793,581 | 1,997 | 8 | 26 | false | true | 4 | UNITS, UNITS, UNITS, UNITS |
We now return to the blanks in discovery mentioned in Sec.1. The blanks have remained inspite of the tremendous activity in HEP in the past two decades. The biggest loophole in standard model is the omission of gravitation, the most important force of nature. Hence, it is now recognized that *Quantum Gravity (QG) is the next frontier of HEP*, and that *the true fundamental scale of physics is the Planck energy 10$^{19}$ Gev*, which is the scale of QG. | 455 | hep-ph/9709212 | 793,604 | 1,997 | 8 | 26 | false | true | 1 | UNITS |
An enforced hadronisation can be a consequence of an external or internal disturbance, leading to an expansion (or split-up) of the object to a density (or mass) well below that for hadronisation. A simple cooling of the object due to Planck radiation will not cause a hadronisation, once we assume that quark matter remains the ground state also at $T = 0$. | 358 | astro-ph/9802236 | 937,105 | 1,998 | 2 | 18 | true | true | 1 | LAW |
: A direct implementation of the idea that the mysteries of quantum gravity and the mysteries of quantum mechanics can be related is Penrose's suggestion that the wave function collapse may be a gravitational phenomenon. Penrose's idea is that there may be a nonlinear dynamical mechanism that forbids quantum superpositions of ("too different") spacetimes. A fact that perhaps supports the speculation is the disconcerting value of the Planck mass. The Planck mass, 22 micrograms, lies approximately at the boundary between the light objects that we see behaving mostly quantum mechanically and the heavy objects that we see behaving mostly classically. Since the Planck mass contains the Newton constant, this coincidence might be read as an indication that gravity plays a role in a hypothetical transition between quantum and classical physics. Consider an extended body with mass $M$ in a quantum superposition of two states $\Psi_{1}$ and $\Psi_{2}$ in which the center of mass is, respectively, in the positions $X_{1}$ and $X_{2}$. Let $U_{grav}$ be the gravitational potential energy that two distinct such bodies would have if they were in $X_{1}$ and $X_{2}$. Penrose suggests that the quantum superposition $\Psi_{1} + \Psi_{2}$ is unstable and naturally decays through some not yet known dynamics to either $\Psi_{1}$ or $\Psi_{2}$, with a decay time FORMULA The decay time (REF) turns out to be surprisingly realistic, as one can easily compute: a proton can be in a quantum superposition for eons, a drop of water decays extremely fast, and the transition region in which the decay time is of the order of seconds is precisely in the regime in which we encounter the boundary between classical and quantum behavior. | 1,730 | gr-qc/9803024 | 951,110 | 1,998 | 3 | 5 | false | true | 3 | UNITS, UNITS, UNITS |
Within the context of supergravity-coupled supersymmetry, fields which are gauge and global singlets are usually considered anathema. Their vacuum expectation values are shifted by quadratically divergent tadpole diagrams which are cutoff at the Planck scale, destabilizing the classical potential and driving the singlet field to large values. We demonstrate a new and generic mechanism which stabilizes the singlet in the presence of an extended gauge symmetry. Such a symmetry will be broken down to the Standard Model by the supergravity interactions near the scale of spontaneous supersymmetry-breaking in the hidden-sector (about 10^{10-11} GeV). The resulting singlet expectation value is stabilized and naturally of order the gravitino mass, providing therefore a weak-scale mass for the Higgs fields of the supersymmetric Standard Model (a "mu-parameter"). The resulting low-energy theory is the minimal supersymmetric Standard Model, with all new fields decoupling at the intermediate scale. | 1,001 | hep-ph/9803310 | 955,073 | 1,998 | 3 | 11 | false | true | 1 | UNITS |
Composite Higgs loop effects in the top mode standard model are discussed by using the Miransky-Tanabashi-Yamawaki (MTY) approach based on the Schwinger-Dyson equation. The top mass is obtained as 179 GeV for the Planck scale cutoff (\Lambda \simeq 10^{19} GeV). This result is different from that of the Bardeen-Hill-Lindner (BHL) approach based on the renormalization group equation (RGE), with QCD plus Higgs loop effects included (m_t \simeq 205 GeV). Detailed comparison of the MTY approach with the BHL approach is made. We derive ``RGE'' from the Pagels-Stokar formula by considering the infrared mass as the ``renormalization point''. Then, it is found that the MTY approach including the composite Higgs loop effects is only partially equivalent to the BHL approach with QCD plus Higgs loop effects. The difference essentially results from the treatment of the composite Higgs propagator, or more precisely, of Z_H^{-1}. Our results can be summarized as m_t (Ours) \simeq 1/\sqrt{2} m_t (MTY), in contrast to m_t (BHL) \simeq \sqrt{2/3} m_t (MTY), where m_t (MTY) \simeq 250 GeV is the original MTY prediction without Higgs loop effects. | 1,146 | hep-ph/9804435 | 992,441 | 1,998 | 4 | 28 | false | true | 1 | UNITS |
Using superfluid phases of $^3$He one can simulate a broad spectrum of phenomena related to the quantum vacuum. We discussed only few of them. On the conceptual level the lessons of $^3$He-A suggest: The gravity is the property of quantum "Planck matter\" in the classical low-energy limit. Gravitational field arise as collective modes of the dynamical deformations of topologically stable gap nodes. The same topological stability provides the zero mass of neutrino, if the overall topological invariant of the "Planck matter\" is nonzero. The equilibrium state of "Planck matter\" does not gravitate, suggesting possible route to solution of cosmological constant problem. The vacuum can be highly unstable behind horizon, and thus can resist to formation of black holes. Fundamental constants $G$ and $c$ should depend on temperature; what about the third fundamental constant -- Planck constant $\hbar$? | 908 | cond-mat/9806010 | 1,022,495 | 1,998 | 6 | 1 | false | true | 4 | UNITS, UNITS, UNITS, CONSTANT |
The low-energy limit of the theory corresponds to the regime when the curvature radius $L$ of the spacetime ${\cal M}$ is much greater than the Planck length $m_{Pl}^{-1}$. In this limit the effective action $\Gamma$ of the theory can be expanded in the curvature. The terms in this series are local and the leading terms can be calculated explicitly. In the linear in curvature approximation $\Gamma$ coincides with the Einstein action [^4] FORMULA Here $dv$ is the volume element of $\partial {\cal M}$. The Newton constant is determined by the following expression FORMULA Here, according to (REF), we put $N=N_s=N_d=N_v$. From this expression it is easy to conclude that at least some of the constituents must be heavy and have mass comparable with the Planck mass $m_{Pl}$. For simplicity in what follows we assume that all the constituents are heavy. | 856 | hep-th/9806078 | 1,033,472 | 1,998 | 6 | 10 | false | true | 2 | UNITS, UNITS |
Case ii), in which $m_{\tilde{q}} \ll m_{\tilde{g}}$, cannot be realized in the framework considered here, in which the soft SUSY breaking terms are introduced at the Planck scale. This is due to the fact that the evolution from the Planck to the electroweak scale forbids such a mass hierarchy. In fact, neglecting the effects of Yukawa couplings and A-terms, one obtains in the down sector the following approximate expression for the ratio $x=m^2_{\tilde{g}}/m_{\tilde{q}}^2$ at the electroweak scale, in terms of the value $x_0$ at the Planck scale [CIT] : FORMULA Even if one starts at the superlarge scale with an extreme hierarchy between squark and gluino masses ($x_0 \gg 1$), at the electroweak scale the two masses will be of the same order. For this reason, we will not consider the case $m_{\tilde{q}} \ll m_{\tilde{g}}$ in our analysis. Case iii), in which $m_{\tilde{q}} \gg m_{\tilde{g}}$, can be realized in some special models, such as effective supersymmetry [CIT] or models with a light gluino [CIT]. However, due to the peculiar features and signatures of these models, a careful analysis of these cases would lie beyond the scope of this paper (see ref. [CIT] for a NLO analysis of $\Delta S=2$ processes in these models). Therefore, in the following we will consider the case $m_{\tilde{q}} \sim m_{\tilde{g}}$, and compare our results with the zeroth- [CIT] and leading-order [CIT] results previously published. | 1,435 | hep-ph/9808328 | 1,093,712 | 1,998 | 8 | 14 | false | true | 3 | UNITS, UNITS, UNITS |
In order to keep the energy finite, which from Eq. REF(#psc){reference-type="eqref" reference="psc"} and on dimensional ground scales as $R_l/l_p^2$, we should also rescale the Planck length (and any other length) as $l_{p,s} = e^{-\beta/2} l_p$. Altogether, M-theory with Planck length $l_p$ on the light-like circle of radius $R_l$ in the momentum $P^+ = \frac{N}{R_l}$ sector is equivalent to M-theory with Planck length $l_{p,s}$ on the space-like circle of radius $R_s$ in the momentum $P=\frac{N}{R_s}$ sector, with FORMULA in the limit $\beta\rightarrow\infty$. Eliminating $\beta$, we obtain the following scaling limit: FORMULA Following Ref. [CIT], we shall denote the latter theory as $\tilde M$ theory. | 714 | hep-th/9809039 | 1,113,130 | 1,998 | 9 | 7 | false | true | 3 | UNITS, UNITS, UNITS |
The Planck satellite will explore a range $\Delta \ln k\simeq 6$ of scales, and will measure $n$ with an accuracy of around $.01$. This means that a scale-dependence $|dn/d\ln k|\mathrel{\rlap{\lower 4pt\hbox{\hskip 1pt$\sim$}} \raise 1pt\hbox{$>$}}2\times 10^{-3}$ should be observable by Planck. | 297 | hep-ph/9809562 | 1,133,890 | 1,998 | 9 | 28 | true | true | 2 | MISSION, MISSION |
Using our cosmological model as given above, we have calculated the expected precision to which $x \equiv \alpha/\alpha_0$ can be determined. The results of this calculation have been shown in Fig. 3 as a function of the maximum measured $l$-value. We note here that $l_{\rm max}({\rm MAP}) \simeq 1000$ and $l_{\rm max}({\rm PLANCK}) \simeq 2500$. Fortunately, since the CMBR spectrum is very sensitive to changes in $x$, it seems possible to detect changes as small as $10^{-3}-10^{-2}$ even if all cosmological parameters must be determined simultaneously. To be on the conservative side we estimate that $\delta x \leq 10^{-2}$ is a realistic obtainable precision. | 668 | astro-ph/9810102 | 1,142,697 | 1,998 | 10 | 7 | true | true | 1 | MISSION |
Allowing for the possibility of large extra dimensions, the fundamental Planck scale $M$ could be anywhere in the range $\TeV\lsim M\lsim \mpl$, where $\mpl=2.4\times 10^{18}\GeV$ is the four-dimensional Planck scale. If $M\sim\TeV$, quantum corrections would not destabilize the Higgs mass even if there were no supersymmetry. But we point out that supersymmetry must in fact be present, if there is an era of cosmological inflation, since during such an era the inflaton mass satisfies $m\ll M^2/\mpl=10^{-15}(M/\TeV)$ and supersymmetry will be needed to protect it. If the inflation hypothesis is accepted, there is no reason to think that Nature has chosen the low value $M\sim \TeV$, however convenient that choice might have been for the next generation of collider experiments. | 784 | hep-ph/9810320 | 1,146,773 | 1,998 | 10 | 11 | false | true | 2 | UNITS, UNITS |
2. Next, we remark in passing on another fascinating connection between the two derived scales, $M_W$ and $M_{Planck}$, which are generated from the two fundamental scales of the model, $M_s$ and $M_c$. If we write $\alpha' \sim 1/M_s^2$ then $M_W$ and $M_{Planck}$ are related one to the other by $M_W= 1/(\alpha 'M_{Planck})$. This is reminiscent of a 'T-duality' relationship, raising the tantalizing speculation that perhaps in some sense the physics at the Fermi scale might turn out to be 'T-dual' to the physics at the Planck scale. | 539 | hep-ph/9810535 | 1,165,990 | 1,998 | 10 | 29 | true | true | 4 | UNITS, UNITS, UNITS, UNITS |
> The hypothesis is considered that the vacuum is a Lorentz non-invariant foam in which translational symmetry is spontaneously broken at the Planck or grand unification scale. This could possibly be observed via Rayleigh scattering of ultrahigh energy quanta, and it appears to be ruled out for spin 1/2 leptons and independently testable for photons. A weaker version of the hypothesis predicts (for otherwise massless neutrinos) irreversible neutrino mixing over a length scale of $l_{Planck}(E_{\nu}/E_{Planck})^{-2}$ in comoving cosmic coordinates for a purely four dimensional universe, and, for neutrinos that have spin 3/2 in a higher dimensional manifold above the energy scale $\eta E_{Planck}$, the mixing is predicted to take place over a scale of $\eta^{-4}$ times this length. Such neutrino mixing might also be observable with atmospheric and solar neutrino experiments. | 885 | astro-ph/9811020 | 1,169,142 | 1,998 | 11 | 2 | true | true | 4 | UNITS, UNITS, UNITS, UNITS |
Using above expressions we find $S/N=8$ for $\Omega_m=0.4$ open model and $S/N=13$ for $\Omega_m=0.2$ open model, both for Planck noise and beam properties using $f_{sky}=0.7$. Corresponding numbers for MAP are 3.5 and 7. Both MAP and Planck will thus be able to usefully constrain open models with $\Omega_m<0.4$, which spans the range of currently favored values of $\Omega_m$. For cosmological constant model the numbers are somewhat lower, Planck gives $S/N=3$ and 6 for $\Omega_m=0.4$ and $\Omega_m=0.2$, respectively, while corresponding MAP numbers are 1 and 2. A positive detection in these models can therefore only be obtained with Planck, unless $\Omega_m$ is very low. One can use the absence or presence of cross-correlation to put constraints on the models. Any detection of the signal with MAP will for example be more easily explained in terms of curvature models than with cosmological constant models, while absence of the signal in Planck will certainly rule out all curvature models of interest, as well as put strong constraints on cosmological constant models. Within the context of more specific models, such as the family of CDM models, one can use the cross-correlation to break the degeneracies present when only the CMB power spectrum constraints are used. The well-known degeneracy between curvature and cosmological constant can for example be broken using this cross-correlation. A more detailed analysis which includes temperature, polarization and convergence information will be presented elsewhere [CIT]. Note that the theoretical limit for signal to noise can be obtained by assuming $\kappa$ is perfectly known and is given by $S/N=\sum_l (2l+1)({\rm Corr}^{T \kappa}_l)^2$. This gives $S/N$ about a factor of 2 higher than our results for Planck above. | 1,789 | astro-ph/9811123 | 1,175,300 | 1,998 | 11 | 8 | true | false | 6 | MISSION, MISSION, MISSION, MISSION, MISSION, MISSION |
A quantum elementary system is described by a complex wave field $\psi (\vec{x}, t)$ which, in the non-relativistic limit, satisfies the Schrödinger equation FORMULA where H is the hamiltonian operator FORMULA $U$ being the (external) potential experienced by the system of mass $m$ (in this paper we use natural units, in which $\hbar, =, c, =, 1$). The complex equation (REF) can be equivalently written as two real equations for the modulus $R$ and the phase $S$ of the function $\psi$: FORMULA The last equation is usually referred to as the continuity equation for the probability density $R^2, =, |\psi|^2$. Instead, eq. (REF) has the form of an Hamilton-Jacobi equation for the characteristic function $S$ of a system described by an effective potential FORMULA The term $Q$ is called the "quantum potential"; it is the only non-classical term (i.e. proportional to the Planck constant) entering in the set of equations (REF),(REF). | 939 | quant-ph/9902019 | 1,262,973 | 1,999 | 2 | 5 | false | true | 1 | CONSTANT |
Note that this relation survives in the Maldacena limit ($\Delta T \Delta U>1$), since FORMULA This explains the dual relation between the two different length scales determined by the mass of the open strings stretched between D-branes, on one hand, and the transverse distance between the branes, on the other. As discussed in [CIT], this elementary property is responsible for explaining some important qualitative aspects of D-brane dynamics in connection with the AdS/CFT(SYM) correspondence and holography. Furthermore, if this relation is applied to D-particles, we can immediately derive the characteristic Planck scale $\ell_P=g_s^{1/3}\ell_s$ of 11 dimensions given only that the mass of a D-particle is of order $1/g_s\ell_s$ by combining with the ordinary quantum mechanical uncertainty relations. This also leads to the holographic property that the minimum bit of information of the quantum state of a D-particle is stored in a cell of the order of the Planck volume in the transverse space in 11 dimensions. | 1,022 | hep-th/9902200 | 1,284,451 | 1,999 | 2 | 26 | false | true | 2 | UNITS, UNITS |
From the PICD, the minimum *SIRTF* background (which occurs at the ecliptic pole for wavelengths considered here), $b(\lambda$) is computed as FORMULA where $B_\lambda (T)$ is the Planck function for a temperature of $T$,K. The first term is due to scattered sunlight from zodiacal dust, the second and third terms to thermal emission from zodiacal and Galactic dust, respectively, and the final term is the cosmic microwave background radiation. This function provides an excellent fit to data from the DIRBE instrument (Hauser 1996). | 535 | astro-ph/9903067 | 1,288,235 | 1,999 | 3 | 3 | true | false | 1 | LAW |
In this paper, we present a simple and systematic method to reproduce these results by using the fluctuation-dissipation theorem [CIT] which is a basis of statistical mechanics for irreversible processes when the systems are slightly away from thermal equilibrium. This theorem states the relation between the spontaneous fluctuation of fields in thermal equilibrium and the irreversible dissipation. Although the fluctuation-dissipation theorem has been formulated by various authors, we adopt the formulation by Callen and Welton [CIT], because their formulation is intuitively understandable and appealing. They showed that a general form of fluctuation-dissipation theorem covers a wide range of phenomena such as the Einstein relation for Brownian motion, the Nyquist formula for voltage fluctuation in conductors, and the Planck distribution for photons. | 860 | hep-th/9903062 | 1,291,848 | 1,999 | 3 | 8 | false | true | 1 | LAW |
Fortunately there are two crucial structural features to be exploited here. As noted above the pointing matrix $A$ is usually very sparse, with only ${\cal N}_{\alpha}$ non-zero entries in each row. For simple scanning strategies such as MAXIMA, BOOMERanG and PLANCK, ${\cal N}_{\alpha} = 1$, with a single 1 in the column corresponding to the pixel being observed. For a differencing experiment such as COBE or MAP, ${\cal N}_{\alpha} = 2$, with a $\pm 1$ pair in the columns corresponding to the pixel pair being observed. Moreover, the inverse time-time noise correlations are (by fiat) both stationary and fall to zero beyond some time-separation much shorter than the duration of the observation FORMULA so that the inverse time-time noise correlation matrix is symmetric and band-diagonal, with bandwith ${\cal N}_{\tau} = 2 \tau + 1$. The second half of table REF shows the impact of exploiting this structure on the cost of each step. The limiting step is now no longer constructing the inverse pixel-pixel noise correlation matrix but solving for the map, which is unaffected by these features. For the same datasets making the map now takes of the order of 3.6 Gb of disc, 7 Gb of RAM, and $7 \times 10^{13}$ operations, or 32 hours of the same CPU time. | 1,264 | astro-ph/9903204 | 1,298,062 | 1,999 | 3 | 13 | true | false | 1 | MISSION |
An unusual point of the inequality (REF) is that the minimal spatial length $\delta x$ has a positive correlation with the time interval $T$. Although it seems as if the left-hand side of (REF) can be made arbitrarily small, we cannot detect an arbitrarily small spatial length scale. To show this, let us suppose a test particle is injected into a system to detect a structure with a length scale $\delta x$ of the system by a collision experiment. Since the speed of the particle is smaller than the speed of light, the collision experiment needs a time longer than $\delta x$. Thus, from (REF), we have FORMULA which dictates that the minimal length detectable is indeed the Planck length $\sqrt{G\hbar}$. | 708 | hep-th/9903146 | 1,303,069 | 1,999 | 3 | 17 | false | true | 1 | STAR |
Before getting into the details of the fermion masses and mixings in the Standard Model, we first discuss in general the possible suppressions of couplings we may get in such a scenario. In addition to the usual Planck mass suppression for the higher dimensional operators, the suppressions may also come from the large volume factor of the extra dimensions and from integrating out the vector-like bulk fields and their Kaluza-Klein excitations. | 446 | hep-ph/9904252 | 1,323,086 | 1,999 | 4 | 6 | false | true | 1 | UNITS |
The graviton including its excitations in the extra dimensions can couple to the SM particles on the brane with an effective strength of $1/M_S$ (instead of $1/M_G$) after summing the effect of all excitations collectively, and thus the gravitation interaction becomes comparable in strength to weak interaction at TeV scale. Hence, it can give rise to a number of phenomenological activities testable at existing and future colliders [CIT]. So far, studies show that there are two categories of signals: direct and indirect. The indirect signal refers to exchanges of gravitons in the intermediate states, while direct refers to production or associated production of gravitons in the final state. Indirect signals include fermion pair, gauge boson pair production, correction to precision variables, etc. There are also other astrophysical and cosmological signatures and constraints [CIT]. Among the constraints the cooling of supernovae by radiating gravitons places the strongest limit on the effective Planck scale $M_S$ of order 50 TeV for $n=2$, which renders collider signatures for $n=2$ uninteresting. Thus, we concentrate on $n\ge 3$. | 1,146 | hep-ph/9904510 | 1,346,584 | 1,999 | 4 | 30 | false | true | 1 | UNITS |
For very light masses ($S>150$), numerical investigations of the ratio $R_Q/R_{cl}$ as a function of redshift $z$, using Eq. (REF) with $\mid \overline{\xi}\mid \simeq 1$, reveal that there are two distinct regimes for which this ratio is close to or larger than 1. The first such regime occurs at extremely high redshifts ($z > 10^{26}$), close to the GUT scale. [In the standard cosmology, the Planck era occurs at a redshift of about $10^{31}$, while the GUT era sets in at a redshift of about $10^{26}$.] It is expected that quantum effects would play a significant role at such high redshifts. The *second*, unexpected regime for which the quantum-vacuum terms become large occurs at relatively low redshifts. This second regime exists only for $\overline{\xi}<0$, and occurs when the factor $1+(1/2)\overline{\xi}(1+z)^3 e^{S-d_m}$ in Eq. (REF) approaches zero. This corresponds to values of $z$ near a redshift $z_j$ given by FORMULA In between these early and late regimes, the quantum contribution to the scalar curvature is extremely small and slowly varying, and the evolution of the universe is well-approximated by its classical evolution. | 1,152 | gr-qc/9905031 | 1,354,052 | 1,999 | 5 | 10 | true | true | 1 | EPOCH |
A simple way to see that the D6 brane worldvolume theory does not decouple from the bulk is to note that now in the decoupling limit we keep $g_{YM}^2 \sim g_s l_s^3$ fixed. When we lift the D6 branes solution to M theory, this means that the eleven dimensional Planck length $l_p^3 = g_s l_s^3$ remains fixed, and therefore gravity does not decouple. Another way to see that gravity does not decouple is to consider the system of D6 branes at finite temperature in the decoupling limit. For large energy densities above extremality, $E/V \gg N/l_p^7$, we need the eleven dimensional description. This is given by an uncharged Schwarzschild black hole at the ALE singularity. The associated Hawking temperature is $T_H \sim 1/\sqrt{Nl_p^9E/V}$ and there is Hawking radiation to the asymptotic region of the bulk eleven dimensional supergravity. Generally, the worldvolume theories of D$p$ branes with $p >5$ do not decouple from the bulk. | 938 | hep-th/9905111 | 1,359,555 | 1,999 | 5 | 14 | false | true | 1 | UNITS |
On the other hand, although the Fokker-Planck method requires more assumptions and approximations, it is much less expensive and gives statistically correct results. These features are critically beneficial, not only when the study is meant for a parameter survey, but also when statistically stable results without random noise are necessary for theoretical analyses. For these reasons, as a first step of our study of the fate of CYCs, we simulate the dynamical evolution of CYCs using Fokker-Planck models. We are planning N-body simulations for a few representative cluster parameter sets in a followup study. | 613 | astro-ph/9905325 | 1,370,244 | 1,999 | 5 | 26 | true | false | 2 | FOKKER, FOKKER |
Crucial to the string interpretation of the Fokker--Planck Hamiltonian is a consistency check, equivalent to diffeomorphism invariance on the string worldsheet [CIT]. In the case of the loop operator, it is a generalization of the derivation given in [CIT] (Sect. 3) that the consistency of the string interpretation is equivalent to the zigzag symmetry of Wilson loops, particularly emphasized by Polyakov [CIT]. The key point to note here is that two Wilson loops $L_{i}, i=1,2$ (which are the strings in this formalism) may join either by an infinitesimal loop attaching to $L_{1}$ leading to contact with $L_{2}$ or vice versa. For the string interpretation, diffeomorphism invariance on the worldsheet implies that the difference between these two amplitudes should vanish. Subtracting the amplitudes for the two processes, we encounter amplitudes involving insertions of infinitesimal back--tracking loops, which are trivial if and only if the zig--zag symmetry holds. | 974 | hep-th/9906052 | 1,382,811 | 1,999 | 6 | 7 | false | true | 1 | FOKKER |
Due to their relative isolation, lack of observable interstellar gas and due to their symmetry globular clusters are well approximated by simplified theoretical models. Since the relaxation timescale is long compared to the dynamical time they develop through a sequence of dynamical (virial) equilibria. The fundamental kinetic equation in such case is the Fokker-Planck equation. The use of this equation for stellar dynamics was inspired by plasma physics [CIT]. Recent models of that type include the effects of anisotropy (differences between radial and tangential velocity dispersion, which can be present even in spherical systems) [CIT]. Another improvement includes for the first time the effect of rotation for those globular clusters which are slightly flattened [CIT]. Also anisotropic gaseous models based on a moment evaluation of the Fokker--Planck equation were successfully used [CIT]. | 902 | astro-ph/9906155 | 1,383,516 | 1,999 | 6 | 8 | true | false | 2 | FOKKER, FOKKER |
FORMULA with Planck mass $m_{pl}$. Numerically, $R_a=1.6\times10^8,M_{12}^{-1},m_5^{-2},\mbox{cm}$ where $M_{12}\equiv M_a/10^{-12},M_{\odot}$ and $m_5\equiv m_a/10^{-5},\mbox{eV}$. A similar formula holds even without the limit but with a minor modification of numerical coefficient. It turns out that the axionic boson stars are "oscillating" with the frequency of $m_a/2\pi$ [CIT]. It has been shown that there are no physically relevant, "static", axionic boson stars. This property is specific in real scalar field. Static solutions of complex boson field representing boson stars are well known to exist [CIT]. | 617 | hep-ph/9906353 | 1,389,412 | 1,999 | 6 | 14 | false | true | 1 | UNITS |
The trends toward the flatter mass function with time are clearly shown in this figure. The global mass function changes slowly in the early phase of the evolution, and rather abruptly in the late phase. The mass function within the half-mass radius changes more rapidly than the global mass function. The model with smaller $\mu$ gives more rapid variation in $\alpha$ with time than that with higher $\mu$, as shown in Figs. REF and REF. We also note here that the behaviour of $\alpha$ for the isotropic Fokker-Planck model is very close to that of the anisotropic model. | 574 | astro-ph/9909006 | 1,470,375 | 1,999 | 9 | 1 | true | false | 1 | FOKKER |
From the point of view of applications to the recently proposed [CIT] large extra dimensions scenario, the most important property of our solutions is that they are characterized by nontrivial "warp factors\" that affect the values of the parameters of the world-volume theories [CIT]. In particular, the usual relation between the four dimensional Planck scale, the 6 dimensional "fundamental\" scale of gravity, and the volume of the compactified space is affected by the presence of the warp factors. This difference can be important if the warp factors significantly deviate from unity (which, in the present framework can only be achieved by fine tuning various parameters) (for related papers with one transverse dimension, see [CIT]). | 741 | hep-th/9909199 | 1,500,063 | 1,999 | 9 | 28 | false | true | 1 | UNITS |
The sensitivity of a $\overline{p}$ decay search to the presence of a CPT violating interaction has been characterized by considering a dimension-$n$ CPT-violating quantum field operator ($n > 4$) with characteristic mass scale $m_X$. Dimensional analysis then provides the estimate [CIT] $m_p \tau_{,\overline{p}} \sim [m_p/m_X]^{2n-8}$, yielding : FORMULA For a given lower limit on $\tau_{,\overline{p}}$ the implied lower limit on $m_X$ is most stringent for $n$ = 5. Note that if $m_X$ is at the Planck scale $(1.2\times 10^{19}$ GeV/$c^2)$ and $n$ = 5, the expected $\tau_{,\overline{p}}$ would be $\sim$ 10 Myr. | 618 | hep-ex/9910013 | 1,509,760 | 1,999 | 10 | 6 | false | true | 1 | UNITS |
We can carry out a Fokker-Planck expansion (eq. [REF]) of the kinetic equation (REF) with the $P(\nu\rightarrow\nu^\prime)$ kernel derived in this paper (eq. [REF]). The coefficients in equation (REF) depend on the moments of the kernel, which are given by equation (REF). As a result, we obtain the generalized (for the mildly relativistic case) Kompaneets equation: FORMULA | 376 | astro-ph/9910280 | 1,518,905 | 1,999 | 10 | 15 | true | false | 1 | FOKKER |
We now introduce a pseudo NG chiral superfield $\Phi(x,\theta)$ whose boson components consist of the axion field ${\cal A}(x)$ and its scalar partner, saxion ${\cal B}(x)$. We consider that the NG superfield is produced by a spontaneous breakdown of some global symmetry at the Planck scale $F_{\cal A} \simeq 2\times 10^{18} {\rm GeV}$, which is explicitly broken by the SU(2) gauge anomaly.[^5] Then, we expect at low energies that the NG superfield $\Phi$ couples to the SU(2) gauge multiplet through the anomaly as FORMULA Here, the axion ${\cal A}(x)$ and saxion ${\cal B}(x)$ fields are an imaginary and a real part of the complex boson component of $\Phi(x,\theta)$, respectively. | 688 | hep-ph/9911324 | 1,550,714 | 1,999 | 11 | 12 | true | true | 1 | UNITS |
We investigate the generation of fields from other fields by scalar coupling assuming the priority of the fields in comparison with their sources. This kind of field generation is only possible for fields with a non-spherical configuration. Therefore, the spherical symmetry of all these fields is generally broken.\ This procedure allows a generation of gravitational fields, which can be described by linear field equations. The strengths of the discussed couplings depend on the energy of the electric or magnetic fields. The maximum coupling strength is determined by the specific electric charge of the lightest charged paricles (electrons and positrons). Thus, we are able to describe interacting electric, magnetic, and gravitational spin-1 fields, as well as their quantization, within a common formalism. For the quantum field theory approach we find that the maximum coupling strength is reached at the Planck energy as one should expect for a quantum field theory of gravitational fields.\ As we have seen, these couplings of two different fields have important consequences for the discrete symmetries. The coupling of gravitational fields with other fields causes an obvious CPT violation.\ Violations of CPT are also conjectured in string field theory [CIT] and in the standard model [CIT].\ However, it seems that for gravitational fields the CPT theorem is not strictly applicable because general relativity is not a Poincaré-invariant theory [CIT]. Thus, our investigations yield to the following conclusions:\ It is known that the CPT-symmetry is conserved for the sources, which always generate spherical fields. However, in our approach the CPT violation occurs through the coupling between the electromagnetic and gravitational fields. Therefore, there must be a difference between the sources, which are surrounded by fields with spherical symmetry, and the fields without spherical symmetry, resulting from our approach. | 1,943 | hep-th/9911250 | 1,569,897 | 1,999 | 11 | 30 | false | true | 1 | UNITS |
Due to the Heisenberg uncertainty principle the scale of energy (frequency) and the lifetime of the unvierse are related as FORMULA the scale of momentum projection $p_x$ and the scale of length $a_x$ are related as FORMULA Thus, within the framework of quantum mechanics, the evolution of the universe is governed by the Heisenberg uncertainty principle. The evolution laws for the scales of energy (frequency) and length are defined by the constant of special relativity $c$ and by the constant of quantum mechanics $\hbar$. The evolution law for scale of length is linear like in the classical physics. Unlike the linear law of evolution for the scale of mass in the classical physics, in the quantum mechanics the law of evolution for the scale of energy (frequency) is inversely linear. Hence one can put the scale of energy (frequency) into correspondence to the scale of mass only in a unique moment of time. Such a moment when the scale of energy (mass) of the classical physics and the scale of energy (frequency) of the quantum mechanics are the same is the Planck time. Thus eq. (REF) holds true at the Planck time. | 1,126 | astro-ph/9912277 | 1,584,733 | 1,999 | 12 | 14 | true | false | 2 | UNITS, UNITS |
A model of reionization is therefore, in principle, eminently testable. Current detections of the first Doppler peak in the CMB's temperature anisotropies limit the total optical depth to electron scattering, $\tau_{e}$, such as may arise from reionization, to be $\tau_e \la 1$ [CIT]. Future experiments such as the *Next Generation Space Telescope (NGST)* or the *Space Infrared Telescope Facility* ($SIRTF$) may detect the high-$z$ sites of reionizing sources (see, e.g., [CIT]), or at least exclude currently viable candidates, while upcoming CMB experiments such as $MAP$ or the PLANCK surveyor can measure $\tau_{e}$ to very high accuracies by combining information from temperature anisotropies and polarization in the CMB. | 730 | astro-ph/9912401 | 1,592,148 | 1,999 | 12 | 18 | true | false | 1 | MISSION |
We consider the evolution of the Affleck-Dine scalar during D-term and F-term inflation and solve the combined slow-roll equations of motion. We show that for a typical case, where both the Affleck-Dine scalar and inflaton initially have large values, in D-term inflation the Affleck-Dine scalar is driven to a fixed value, with only a very slight dependence on the number of e-foldings. As a result, there is a definite prediction for the ratio of the baryonic isocurvature perturbation to the adiabatic perturbation. In minimal (d=4) Affleck-Dine baryogenesis the relative isocurvature contribution to the CMB angular power spectrum amplitude is predicted to be in the range $0.01-0.1$, which can account for present large-scale structure observations and should be observable by PLANCK. In a very general case, scale-invariance of the adiabatic perturbations from the Affleck-Dine scalar imposes a lower bound of about 0.01 for d=4. For d=6 the isocurvature perturbation may just be observable, although this is less certain. We also consider F-term inflation and show that the magnitude of the baryonic isocurvature perturbation is fixed by the value of $H$ during inflation. For typical values of $H$ the isocurvature perturbation could be close to present observational limits. | 1,283 | hep-ph/9912478 | 1,596,201 | 1,999 | 12 | 22 | true | true | 1 | MISSION |
A fundamental problem in supergravity and superstring theories is the stabilization of moduli fields, particularly the dilaton. Perturbatively, $\Phi\equiv {\rm exp}(\lambda \phi)$ (the dilaton) has no potential, although it does not behave as a free field because it has non-linear couplings to the kinetic energy of the axion field. (Throughout this paper, we use $\Phi$ and $\phi$ interchangeably to represent the dilaton according to convenience; the constant $\lambda = \sqrt{16 \pi}/m_{pl}$, where $m_{pl}\equiv 1.2 \times 10^{19}$ GeV is the Planck scale, is chosen so that $\phi$ has a canonical kinetic energy density, $\frac{1}{2} \dot{\phi}^2$.) A non-perturbative potential can be induced by gaugino condensates [CIT]. With several gaugino condensates, parameters can be tuned so that there is a locally stable minimum with zero cosmological constant [CIT]. See the solid curve in Fig. 1. However, the potential is exponentially steep ($V\sim \exp (-\exp (\phi))$) and the desired minimum, $\Phi_{min}$, is separated by an exponentially small barrier (compared to the Planck scale) from an observationally unacceptable anti-de Sitter vacuum [CIT]. It appears that, unless the initial conditions of the dilaton field are finely-tuned to lie very near the correct minimum, the field will overrun or miss altogether the desired minimum. | 1,345 | hep-th/0001112 | 1,625,324 | 2,000 | 1 | 19 | true | true | 2 | UNITS, UNITS |
In recent work on experimental tests of quantum-gravity-motivated phenomenological models, a significant role has been played by the so-called ``$\kappa$'' deformations of Poincar\'e symmetries. Sensitivity to values of the relevant deformation length $\lambda$ as small as $5 \cdot 10^{-33}m$ has been achieved in recent analyses comparing the structure of $\kappa$-Poincar\'e symmetries with data on the gamma rays we detect from distant astrophysical sources. We investigate violations of CPT symmetry which may be associated with $\kappa$-Poincar\'e in the physics of the neutral-kaon system. A simple estimate indicates that experiments on the neutral kaons may actually be more $\lambda$-sensitive than corresponding astrophysical experiments, and may already allow to probe values of $\lambda$ of order the Planck length. | 828 | hep-ph/0001305 | 1,634,987 | 2,000 | 1 | 28 | false | true | 1 | UNITS |
The above procedure of $T$ dualization has the nice property to lead to a finite $D-1$ dimensional Planck mass. Indeed, whereas in the original solution it would be: FORMULA which diverges near infinity, our solution that throws away the region near infinity and paste a copy of the region near the origin, naturally gives a finite $D-1$ dimensional Planck mass[^3]: FORMULA At this stage, the position $r_\circ$ of the fixed point under the $T$ symmetry is arbitrary. It is believed that a dynamical description of the brane beyond its effective description in terms of a cosmological constant (REF) should allow to stabilize the value of $r_\circ$. Notice that, when $r_\circ=R_{\scriptscriptstyle AdS}$, the expression (REF) coincides with the Planck mass on the brane computed in the RS model. | 797 | hep-th/0002130 | 1,659,524 | 2,000 | 2 | 16 | false | true | 3 | UNITS, UNITS, UNITS |
Future CMB missions such as MAP and Planck could strengthen these constraints considerably. The optical depth resolution of MAP is expected to be 0.022, and of Planck is expected to be 0.004 (Zaldarriaga, Spergel, & Seljak 1997; Bouchet, Prunet, & Sethi 1999; Eisenstein, Hu, & Tegmark 1999). Since the existence of a Ly$\alpha$ emitter at $z=5.64$ (see Haiman & Spaans 1999) shows that reionization must have occurred before then, this means that both satellites, and especially Planck, will be able to detect the effects of ionization regardless of the actual redshift of reionization. If $z_{\rm reion}\sim 10$ then the redshift of reionization could even be determined directly with SIRTF or NGST via, e.g., analysis of the damping wing of the Gunn-Peterson trough (Miralda-Escudé 1998) or detection of transmitted flux between Lyman resonances (Haiman & Loeb 1999). The upper limit on the product $\epsilon_{-1}(M/M_\odot)f_{\rm CO}$ scales like $\tau_{\rm scatt}^2$ (or, for $z\gg 1$, like $z_{\rm reion}^3$), so if $z_{\rm reion}\sim 10$ this upper limit is decreased by almost a factor of 100. In this case, barring extremely inefficient accretion, dark matter must be composed of less compact objects or of WIMPs. | 1,222 | astro-ph/0003176 | 1,683,885 | 2,000 | 3 | 13 | true | false | 3 | MISSION, MISSION, MISSION |
Most measurements of small-angle CMB anisotropy are being done at high radio frequencies (in the 15--90 GHz range) where Galactic and extragalactic contaminants are a minimum. However, the high-frequency detections of small-angle anisotropy, which have to-date been Sunyaev-Zeldovich (S-Z) decrements towards clusters of galaxies, have been difficult measurements made with long integrations and using telescopes with small fields-of-view. All-sky images of CMB anisotropies with 10's of arcmin resolution are expected to become available in the coming decade from the $MAP$ and $PLANCK$ satellite missions; however, they are expected to detect S-Z anisotropies from only the relatively high-mass and nearby S-Z clusters. The next generation of high-brightness-sensitive imaging arrays, like the CBI and AMIBA, which are specifically designed for surveys for S-Z clusters, are also expected to cover only small sky areas because of their small fields of view. | 959 | astro-ph/0003227 | 1,687,742 | 2,000 | 3 | 15 | true | false | 1 | MISSION |
However, rather than proceeding with a plain fit of a "ad hoc"number of black bodies, we have preferred to use an inversion method to analize the SEDs of the galaxies in the sample. This has the advantage that no assumptions have to be made as to the number or location of the sources responsible for the observed spectrum. In particular, we have used an Inverse Planckian Transform algorithm, that employs an emissivity ($\epsilon \propto \lambda^{-1.5}$) weighted Planck function kernel to switch from frequency space to the temperature domain, hence revealing the temperature distribution of the sources that originate the observed SEDs. The method applies Bayes theorem of conditional probability and the Richardson-Lucy iteration algorithm which converges quickly to a optimum result. To increase the number of data points used in the inversion algorithm, whenever available, we have added the four IRAS band fluxes at 12, 25, 60 and 100 $\mu$m as given by Edelson, Malkan & Rieke (1987). Furthermore, to avoid boundary convergence problems in the inversion algorithm we have used 10 $\mu$m ground-based data from several authors (Rieke 1978; Edelson, Malkan & Rieke 1987; Maiolino et al 1995), and 1.3 mm upper limit data from Edelson, Malkan & Rieke (1987). These additional data have been used solely for the purpose of constraining the inversion algorithm at the borders of the wavelength range of interest. Details of this method are given in Salas (1992) and in Pérez Garcı́a, Rodrı́guez Espinosa, & Santolaya Rey (1998) and are not repeated here. | 1,558 | astro-ph/0003349 | 1,696,596 | 2,000 | 3 | 23 | true | false | 1 | LAW |
In conclusion, though Kerr's metric for rotating black holes is rightly celebrated as one of the landmark discoveries of 20th century science, the subsequent failure to satisfactorily unite the classical theory of general relativity with quantum mechanics remains a severe impediment to an understanding of nature. Until this fundamental obstacle can be overcome, one must be fully aware of the inherent drawbacks of myopic alternatives. Black hole topology is a subject unsuitable for purely classical computations, however sophisticated the mathematical veneer. Extreme caution should be employed if results are to be usefully construed. The rule of thumb calculations presented here are suggestive that an ultimate theory might accommodate the possibility of toroidal black holes, temporarily stabilised on astrophysically relevant timescales by the action of accretion, tidal deformation and Planck scale repulsion. The basis of the scenario advocated for supporting TBH stability is summarised below: | 1,005 | astro-ph/0004051 | 1,708,991 | 2,000 | 4 | 4 | true | false | 1 | UNITS |
- $3 \frac{1}{2}$ decades in energy reach would explore more than 20% of the log-energy gap from our current experimental reach all the way up to the Planck mass scale, at $10^{19}$ GeV. The Planck scale is defined by where quantum gravitational effects necessarily become important enough that even the framework for our current theories no longer makes sense and some theory that would surely be a close approximation to the Theory of Everything would be required to describe the physical processes. By biting off a significant fraction of this log-energy span we would presumably be giving ourselves a good shot at such an elevated level of understanding of our Universe. | 674 | hep-ex/0005008 | 1,740,198 | 2,000 | 5 | 4 | false | true | 2 | UNITS, UNITS |
On ${\cal H}_G$ we introduce multiplication and derivative operators on the dense domain ${\cal D}:=C^\infty(G)$ by FORMULA where $h_{AB}$ denote the matrix elements of the defining representation of $G$ and $i,j,k,..=1,2,..,\dim(G)$ and $X_j(h)=\mbox{tr}([\tau_j h]^T\partial/\partial h)$ denotes the generator of right translations on $G$ into the $j$'th coordinate direction of $Lie(G)$, the Lie algebra of $G$. We choose a basis $\tau_j$ in $Lie(G)$ with respect to which tr$(\tau_j \tau_k)=-N\delta_{jk},\; [\tau_j,\tau_k]=2f_{jk}\;^l \tau_l$ where $N-1$ is the rank of $G$. The operators (3.2) enjoy the canonical commutation relations FORMULA mirroring the classical Poisson brackets FORMULA on the phase space $T^\ast G$, the cotangent bundle over $G$, where $s$ plays the role of Planck's constant. It is easy to check that the CCR of (3.3) and the adjointness relations coming from $\overline{p}_j=p_j,\;\overline{h_{AB}}=f_{AB}(h)$ are faithfully implemented on ${\cal H}_G$. Here, $f_{AB}$ depends on the group, e.g. $f_{AB}(h)=(h^{-1})_{BA}$ for $G=SU(N)$, and $\hat{p}_j$ is essentially self-adjoint with core $\cal D$. | 1,133 | hep-th/0005235 | 1,765,436 | 2,000 | 5 | 25 | false | true | 1 | CONSTANT |
The implementation of a Planck-scale high frequency and short wavelength cutoff in quantum theories on expanding backgrounds may have potentially nontrivial implications, such as the breaking of local Lorentz invariance and the existence of a yet unknown mechanism for the creation of vacuum modes. In scenarios where inflation begins close to the cutoff scale, these effects could have observable consequences as trans-Planckian modes are redshifted to cosmological scales. In close analogy with similar studies of Hawking radiation, a simple theory of a minimally coupled scalar field in de Sitter space is studied, with a high frequency cutoff imposed by a nonlinear dispersion relation. Under certain conditions the model predicts deviations from the standard inflationary scenario. We also comment on the difficulties in generalizing fluid models of Hawking radiation to cosmological space-times. | 901 | astro-ph/0005533 | 1,765,995 | 2,000 | 5 | 26 | true | true | 1 | UNITS |
In the shaded area of Fig. REF (left plot) magnetic fields are produced with growing frequency spectrum. In the shaded area of the right plot of Fig. REF magnetic fields are produced with decreasing frequency spectrum. The theoretical bias would point, a priori, towards increasing frequency spectra. In fact in this case the two-point functions are decreasing at large distance scales. However, in the present analysis all the possibilities should be borne in mind. The full (thin) line appearing in both plots of Fig. REF denotes a less conservative magnetogenesis requirement and it corresponds to larger a dynamo amplification rate. The thin curve can be obtained by requiring, from Eq. (REF), $r(\omega_{G}) > 6.07 \times10^{-50}$ which corresponds to $\Gamma^{-1} \sim 0.5$ Gyr. According to Fig. REF reasonable seeds are produced provided $n\beta$ is larger than $0.6$. The four dimensional Planck mass should be small in units of the fundamental Planck mass. The parameter space seems to select typical values of $M_{4}$ between $10^{13}$ Tev and $10^{3}$ TeV. | 1,068 | hep-ph/0007163 | 1,820,295 | 2,000 | 7 | 15 | true | true | 2 | UNITS, UNITS |
Therefore, in the context of the standard model extension of Kostelecký and co-workers [CIT], our ${}^{129}$Xe/${}^{3}$He maser measurement improves the constraint on $\tilde{b}^n_J$ to nearly $10^{-31}$ GeV, or more than six times better than the ${}^{199}$Hg/${}^{133}$Cs clock comparison [CIT]. Note that the ratio of this limit to the neutron mass ($10^{-31} \mathrm{GeV}/m_n \sim 10^{-31}$) compares favorably to the dimensionless suppression factor $m_n / M_{\mathit{Planck}} \sim 10^{-19}$ that might be expected to govern spontaneous symmetry breaking of LLI and CPT originating at the Planck scale. We expect more than an order of magnitude improvement in sensitivity to LLI/CPT--violation of the neutron using a new device recently demonstrated in our laboratory: the ${}^{21}$Ne/${}^3$He Zeeman maser. | 812 | physics/0007063 | 1,825,194 | 2,000 | 7 | 18 | false | true | 2 | UNITS, UNITS |
The purpose of this article is to discuss the transition from the Planck epoch to the period when classical gravity prevailed. Some qualitative statements can be made but we will mostly be concerned with defining an order parameter to probe this region and with making estimates about its behavior to determine whether a phase transition took place. We shall also briefly discuss our ideas in string theory. | 407 | gr-qc/0007054 | 1,829,308 | 2,000 | 7 | 21 | false | true | 1 | EPOCH |
In the case of strong X-ray irradiation ($\Gamma =1000$) the surface layer is significantly hotter than the disk (Fig. 8, right panel). Temperature inversion is stronger for larger incident angles. As the Planck function of the temperature-inversion layer is greater than the Planck function of the disk where the optical depth is equal to unity, the lines are in emission. | 373 | astro-ph/0008016 | 1,841,599 | 2,000 | 8 | 1 | true | false | 2 | LAW, LAW |
The answer to this essential question is in principle in the affirmative, since the pre-Big Bang scenario incorporates a dilaton field coupled to the metric, which modifies the evolution of tensor perturbations. It is well known, indeed, that the transition from an inflationary period to the FRW radiation-dominated era is associated with the production of a background of relic gravitational waves. Such primordial signals decoupled from matter soon after the Planck era and, unlike electromagnetic radiation which underwent a complicated history until recombination, gravitons have been transmitted scarcely without interaction down to our present epoch. As a consequence, their present spectrum should be a faithful portrait of the very early universe, thus opening a window for the observation of processes occurring near the Planck scale, and for discriminating among various theories of high-energy models of cosmology and of unified interactions. With respect to the standard inflationary scenario, the amplification of tensor perturbations in the pre-Big Bang scenario is strongly enhanced in the limit of large frequencies [CIT], and the amplitude of the spectrum is normalised so as to match the string scale at the high-frequency end point of the spectrum [CIT]. As a result, it has been claimed [CIT] that the produced background of gravitational waves could be detected in the near future by various experiments such as the second (planned) generation of interferometric detectors [CIT]. | 1,501 | hep-th/0010085 | 1,921,169 | 2,000 | 10 | 11 | false | true | 2 | EPOCH, UNITS |
The cosmological constant was introduced by Einstein in 1917 to make the universe static, since it appeared at that time that the universe seemed to be not evolving. But the discovery of the expanding universe in 1929 did not need a static universe, and the cosmological constant has become another parameter in general relativity. We expect that if a theory describes physics at the mass scale of order $m$, then parameters in the theory are expected to be of order $m$. Gravitation is described at the Planck scale(or inverse Newton's constant) of order $10^{19}$ GeV. However, the cosmological constant appearing in the gravity equation is phenomenologically very strongly bounded $<(0.01 {\rm eV})^4$, which implies that there is a hierarchy of order $10^{-120}$ between parameters in the gravity theory. This hierarchy problem could have been questioned even at the time of Einstein, not from the static universe condition but as an hierarchy problem. | 956 | hep-th/0011118 | 1,964,655 | 2,000 | 11 | 14 | true | true | 1 | UNITS |
The simulations presented in this paper were carried out on the T3E supercomputer at the Computing Centre of the Max-Planck-Society in Garching, Germany. We are grateful for the hospitality of the Institute for Theoretical Physics at Santa Barbara, where much of the final writing of this paper was completed. | 309 | astro-ph/0012055 | 1,988,473 | 2,000 | 12 | 3 | true | false | 1 | MPS |
One stringent constraint in any cosmological models is nucleosynthesis. It must take place in the conventional radiation dominant era to explain the present amount of light elements. Therefore, $T_c$ must be higher than the temperature at nucleosynthesis, $T_{\rm NS} \sim$ 1 MeV. This constraint implies $m_5 > 1.6 \times 10^4,(g/100)^{1/6} (T_{\rm NS}/$ 1MeV$)^{2/3}$ GeV, which is included in Fig. 1. The r.h.s. of the vertical line is the allowed region. If the second Randall-Sundrum model turns out to be a fundamental theory, in order to recover the Newtonian force above 1mm scale, the 5-dimensional Planck mass is constrained as $m_5 \geq 10^8$ GeV [CIT], which is satisfied in the r.h.s. region of the dotted vertical line in Fig. 1. | 743 | astro-ph/0012313 | 2,004,997 | 2,000 | 12 | 14 | true | true | 1 | UNITS |
We now redefine the field $\hat \phi_i=\sqrt{A\left(L_i\right)}\phi_i$ to absorb the factor $A\left(L_i\right)$ in the kinetic term of the Lagrangian ${\bf L}_i$, so the effective 4-D low energy action becomes FORMULA where $m_{Hi}^2=A(L_i)M_{Hi}^2$ and $m_{ci}^2=A(L_i) M_{ci}^2$. It is important to note that the Newton's constant and the effective cosmological constant $\Lambda_{eff}$ are the same everywhere, so observers on the Planck (hidden) brane see the same $G_N$ and $\Lambda_{eff}$ as observers on the TeV (visible) brane, even if the visible brane tension is negative, as is the case in the Randall-Sundrum model. To be more realistic, ${\bf L}_{visible}$ may be replaced by the standard model Lagrangian density. In ${\bf S}^{\left(4\right)}$, we have also included a conformal field theory term ${\bf L}_{CFT}$. Using the AdS/CFT correspondence [CIT], the effect of the Kaluza-Klein (KK) gravity modes may be incorporated into a conformal field theory on the brane. This should be the case when the model covers the region between particle horizons, where the gravity KK modes have a continuous mass spectrum. In the orbifold model, where the gravity KK modes may be discrete, in which case ${\bf L}_{CFT}$ should be replaced by another appropriate strongly interacting field theory. | 1,299 | hep-th/0012129 | 2,006,588 | 2,000 | 12 | 14 | true | true | 1 | BRANE |
The first terms here ($\tilde{m}^2$) are the soft ones, which are calculated using the RG equations starting from their values at the GUT (Planck) scale. The second ones are the usual masses of quarks and leptons and the last ones are the $D$ terms of the potential. | 266 | hep-ph/0012288 | 2,016,895 | 2,000 | 12 | 21 | false | true | 1 | UNITS |
[^1]: While it is clear that a truly fundamental role for the Planck length in space-time structure is inconsistent with the combination of the Relativity Principle and ordinary Fitgerald-Lorentz length contraction, it is of course possible [CIT] that the Planck length be associated with some sort of background in a way that is consistent with both the Relativity Principle and Fitgerald-Lorentz length contraction. This would be analogous to the well-known special-relativistic description of the motion of an electron in a background electromagnetic field. This physical context is described by different observers in a way that is consistent with the Relativity Principle, but only when these observers take into account the fact that the background electromagnetic field also takes different values in different inertial frames. The electric and the magnetic components of the background field are not observer-independent, but their combination affects the motion of the electron in a way that is of course consistent with the Relativity Principle. The Planck length could play a similar role in fundamental physics, *i.e.* it could reflect the properties of a background, but then the presence of such a background would allow to single out a "preferred\" class of inertial frames for the description of the short-distance structure of space-time. In the present study I show that in addition to this scenario, which introduces the Planck length together with a preferred class of inertial frames, it is also possible to follow another scenario for the introduction of the Planck length: this second option does not predict preferred inertial observers but does require a short-distance deformation of FitzGerald-Lorentz contraction. | 1,741 | hep-th/0012238 | 2,021,028 | 2,000 | 12 | 26 | false | true | 5 | UNITS, UNITS, UNITS, UNITS, UNITS |
The observational bound on the cosmological constant is FORMULA where $M_{Pl}$ is the Planck mass (of about $10^{19}$ GeV) and the formula has been written in such a way that the quantity appearing on the left hand side corresponds to the vacuum energy density. This is a very small quantity once one admits the possiblilty of the Planck scale as the fundamantal scale of physics. Even in the particle physics standard model of weak, strong and electromagnetic interactions one would expect a tree level contribution to the vacuum energy of order of several hundred GeV taking into account the scalar potential that leads to electroweak symmetry breaking. Moreover, in quantum field theory we expect additional contributions from perturbative corrections, e.g. at one loop FORMULA in addition to $\lambda_0$ the bare (tree level) value of the cosmological constant which can in principle be chosen by hand. The supertrace in (REF) is to be taken over degrees of freedom which are light compared to the scale set by the UV-cutoff. Comparison of (REF) with (REF) shows that one needs to fine-tune 120 digits in $\lambda_0 M_{Pl}^2$ such that it cancels the one-loop contributions with the necessary accuracy. Supersymmetry could ease this problem of radiative corrections (for a review see [CIT]). If one believes that the world is supersymmetric above the TeV scale one would still need to adjust 60 digits. Instead of adjusting input parameters of the theory to such a high accuracy in order to achieve agreement with observations one would prefer to get (REF) as a prediction or at least as a natural result of the theory (in which, for example, only a few digits need to be tuned, if at all). | 1,694 | hep-th/0012265 | 2,024,496 | 2,000 | 12 | 29 | false | true | 2 | UNITS, UNITS |
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Dataset Card for the Astro-HEP-Planck Corpus
Astro-HEP-Planck Corpus contains 1,494 paragraphs from arXiv papers relating to astrophysics or high energy physics together with word-sense labels for 2,932 occurrences of "Planck".
This table details the main columns of the dataset:
| Column | Description |
|---|---|
| text | Full text of the paragraph |
| length | Number of unicode characters in the paragraph |
| arxiv_id | The arXiv identifier of the paper from which the paragraph was taken |
| text_id | ID of the text/paragraph |
| year | Year of publication of the arXiv paper |
| month | Month of publication of the arXiv paper |
| day | Day of publication of the arXiv paper |
| astro | Whether or not the paper relates to astrophysics |
| hep | Whether or not the paper relates to high energy physics |
| num_planck_labels | Number of labeled occurrences of "Planck" in the paragraph |
| planck_labels | List of word-sense labels for the occurrences of "Planck" in the paragraph |
The primary purpose of the Wikipedia-Physics Corpus lies in its use for analyzing the meaning of concepts in physics. For further insights into the corpus and the underlying research project (Network Epistemology in Practice) please refer to this paper:
Construction
The paragraphs were randomly sampled from the subset of paragraphs in the Astro-HEP Corpus containing the term "Planck".
Occurrences of "Planck" were identified using a case-insensitive regular expression to capture variations like "PLANCK" and "Planck(2015)"" while excluding forms like "planckian". The labels denote distinct meanings of the target term, such as PERSON, CONSTANT, UNITS, LAW, MPS, MISSION, and FOKKER.
Details
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- Funded by: The European Union under Grant agreement ID: 101044932
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