Shortest scale of quantum field theory

Brustein, Ram; Eichler, David; Foffa, Stefano; Oaknin, David H.

doi:10.1103/physrevd.65.105013

Cited by 27 publications

(42 citation statements)

References 19 publications

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“…A bound of the same form was previously proposed in [4] and [17], and independent arguments in support of bounds of this sort have also been recently put forward [18], [19].…”

Section: Ceb Vs Cftmentioning

confidence: 60%

CFT, holography, and causal entropy bound

2001

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The causal entropy bound (CEB) is confronted with recent explicit entropy calculations in weakly and strongly coupled conformal field theories (CFTs) in arbitrary dimension D. For CFT's with a large number of fields, N , the CEB is found to be valid for temperatures not exceeding a value of order M P /N 1 D−2 , in agreement with large N bounds in generic cut-off theories of gravity, and with the generalized second law. It is also shown that for a large class of models including high-temperature weakly coupled CFT's and strongly coupled CFT's with AdS duals, the CEB, despite the fact that it relates extensive quantities, is equivalent to (a generalization of) a purely holographic entropy bound proposed by E. Verlinde.

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“…A bound of the same form was previously proposed in [4] and [17], and independent arguments in support of bounds of this sort have also been recently put forward [18], [19].…”

Section: Ceb Vs Cftmentioning

confidence: 60%

CFT, holography, and causal entropy bound

2001

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“…A bound of the same form was previously proposed in [9] and [32], and independent arguments in support of bounds of this sort have also been put forward in [13].…”

Section: A Radiation Dominated Universementioning

confidence: 73%

Cosmological Entropy Bounds

Brustein

Lecture Notes in Physics

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I review some basic facts about entropy bounds in general and about cosmological entropy bounds. Then I review the Causal Entropy Bound, the conditions for its validity and its application to the study of cosmological singularities. This article is based on joint work with Gabriele Veneziano and subsequent related research. I. TO GABRIELEOn the occasion of your 65th birthday may you continue to find joy in science and life as you have always had, and continue to help us understand our universe with your creative passion and vast knowledge. It is a pleasure and an honor to contribute to this volume and present one of the subjects among your many interests. Thank you for explaining to me why entropy bounds are interesting and for your collaboration on this and other subjects. II. INTRODUCTION A. What are entropy bounds?The second law of thermodynamics states that the entropy of a closed system tends to grow towards its largest possible value. But what is this maximal value? Entropy bounds aim to answer this question.Bekenstein [1] has suggested that for a system of energy E whose size R is larger than its gravitational radius R > R g ≡ 2G N E, entropy is bounded by S ≤ ER/h = R g R l −2 P .Here l P is the Planck length. This is known as the Bekenstein entropy bound (BEB).Entropy bounds are closely related to black hole (BH) thermodynamics and their interplay with their "normal" environment. They are also probably associated with instabilities to forming BH's, however, this has not been proved in an explicit calculation. The original argument of Bekenstein was based on the Geroch process: a thought experiment in which a small thermodynamic system is moved from infinity into a BH. The small system is lowered slowly until it is just outside the BH horizon, and then falls in. By requiring that the generalized second law (GSL) will not be violated one gets inequality (1).A long debate about the relationship between entropy bounds and the GSL has been going on. On one side Unruh, Wald and others [2,3] have argued that the GSL holds automatically, so that entropy bounds cannot be inferred from situations where the law seems to be violated. They argue that the microphysics will eventually take care of any apparent violation. Consequently, they argued that the BEB does not have to be postulated as a separate requirement in addition to the GSL. Responding to their arguments Bekenstein 2[4] has argued that it is not always obvious in a particular example how the system avoids violating the bound and analyzed in detail several of the purported counterexamples of this type and demonstrated in each case the specific mechanism enforcing the bound.Holography [5] (see below) suggests that the maximal entropy of any system is bounded by S HOL ≤ Al −2 P , where A is the area of the space-like surface enclosing a certain region of space. For systems of limited gravity R > R g , and since A = R 2 , the BEB implies the holography bound. Physics up to scales of about 1 TeV is very well described in terms of quantum field theory,...

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“…As noticed in [1], if V is the whole box then the vacuum |0 of the system is an eigenstate of H V , so it does not fluctuate. For partial volumes whose typical size V 1/3 is parametrically larger than the ultraviolet cutoff X/N, the vacuum |0 is no longer an eigenstate of H V , and therefore H V fluctuates quantum mechanically.…”

Section: Collective Observables and Classical Dynamics Of Their Qmentioning

confidence: 98%

“…As another concrete illustration of our formalism and for a more detailed discussion of lifetimes of quantum fluctuations of collective observables let us consider the collective operator (introduced in [1]),…”

Section: Collective Observables and Classical Dynamics Of Their Qmentioning

confidence: 99%

“…Similarly, quantum fluctuations can affect spacetime curvature. In this context, the possible gravitational collapse of strong quantum fluctuations towards black holes was considered recently [1], as well as issues concerning classicality and decoherence of quantum fluctuations [2,3] during and after inflation, and their time evolution [4,5]. Additionally, the possible dissipative effects [6] of vacuum fluctuations on arbitrary motions in the vacuum were considered.…”

Section: Introductionmentioning

confidence: 99%

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Classical dynamics of quantum fluctuations

Brustein

Oaknin

2003

Phys. Rev. D

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It is shown that the vacuum state of weakly interacting quantum field theories can be described, in the Heisenberg picture, as a linear combination of randomly distributed incoherent paths that obey classical equations of motion with constrained initial conditions. We call such paths "pseudoclassical" paths and use them to define the dynamics of quantum fluctuations. Every physical observable is assigned a timedependent value on each path in a way that respects the uncertainty principle, but in consequence, some of the standard algebraic relations between quantum observables are not necessarily fulfilled by their time-dependent values on paths. We define "collective observables" which depend on a large number of independent degrees of freedom, and show that the dynamics of their quantum fluctuations can be described in terms of unconstrained classical stochastic processes without reference to any additional external system or to an environment. Our analysis can be generalized to states other than the vacuum. Finally, we compare our formalism to the formalism of coherent states, and highlight their differences.

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Shortest scale of quantum field theory

Cited by 27 publications

References 19 publications

CFT, holography, and causal entropy bound

CFT, holography, and causal entropy bound

Cosmological Entropy Bounds

Classical dynamics of quantum fluctuations

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