The second law of thermodynamics, TCP and Einstein causality in anti-de Sitter spacetime

Buchholz, Detlev; Florig, Martin; Summers, Stephen J.

doi:10.1088/0264-9381/17/2/102

Cited by 28 publications

(62 citation statements)

References 10 publications

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“…As a matter of fact, for the case of the Unruh effect in Minkowski spacetime, the first general proof of the corresponding KMS-property for general interacting fields has been given in [14] by alternative methods based on operator algebras. In this connection one should also quote other presentations and analyses of the generalized Unruh effect in the approach of algebraic QFT, in particular those of [15] for de Sitter and [16] for anti-de Sitter (see also [17]). However, we did not pretend to give here a survey of all the investigations and possible viewpoints concerning the Unruh-type phenomenons.…”

Section: Thermal Propertiesmentioning

confidence: 99%

Thermal Aspects in Quantum Field Theory

Bros

2003

Ann. Henri Poincaré

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Thermal (or "KMS") states as well as ground states are characterized by analyticity properties in the (complexified) time variable. Such a characterization is applied to the quantum field theoretical systems on Minkowski, de Sitter and anti-de Sitter spacetimes. Privileged theories (or "vacua") can be defined on the basis of general principles which ensure "maximal" analyticity properties of the correlation functions. In such theories, there exists an observer-dependent thermal interpretation of the "vacuum" which is due to the (complex) geometry. In Minkowski spacetime, the (non-privileged) thermal quantum field theories at arbitrary temperature are investigated for their particle aspect at asymptotic times. This aspect is encoded in the corresponding two-point functions through a certain "damping factor", which is shown to depend on the dynamics of the interacting fields and suggests a possible substitute to the usual pole-particle concept in the thermal case.The first part of this talk (Sec 1-3) will be devoted to the following question: how does one determine the properties of stability of quantum states for relativistic systems which are described by local quantum fields, either in the Minkowskian background of flat spacetime, or more generally in certain curved spacetimes of simple type considered as given backgrounds for the quantum systems?. There is a general result of Pusz and Woronowicz [8] on quantum systems, according to which the class of quantum states satisfying an appropriate criterion of stability (called "passivity") can be partitioned into two subclasses, namely, on the one hand the "ground states" and on the other hand the "thermal equilibrium states" or "KMS states"; both cases are characterized by specific analyticity properties in the time-variable of the correlation functions of all pairs of local observables of the system. When one deals with a relativistic system in which the local observables are described in terms of quantum fields, it turns out that the "ground-state" or "thermal-state" interpretation of a stable state of the theory will in general depend on the motion of the local observer. While this phenomenon already occurs in flat spacetime with the Unruh effect [9], it seems to acquire a more general validity in curved spacetime by appearing as the manifestation of a certain type of "temporal curvature" of the world lines which is felt as a thermal effect by the corresponding observer. In models of spacetime equipped with a maximal symmetry group such as Minkowski, de Sitter and anti-de Sitter spacetimes, a specially * The results presented in the first part of this talk have been obtained in joint works with

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Section: Thermal Propertiesmentioning

confidence: 99%

Thermal Aspects in Quantum Field Theory

Bros

2003

Ann. Henri Poincaré

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“…Despite such difficulties it has been argued that, under reasonable boundary conditions, thermality of its vacuum state still arises, but only for accelerations above a critical acceleration of √ | |/3. In particular, this result has been argued in [21], where they consider the 4-dimensional thermal responses in both de Sitter and AdS spacetime, and also shown to hold in a more general field theory framework [31][32][33].…”

Section: Scalar Fields In D-dimensional Anti-de Sitter Spacetimementioning

confidence: 62%

“…Indeed, it was shown [21,22] that thermality arises in the free field case only for accelerations above the mass scale of the AdS curvature. This result was later generalized in a more rigorous setting [31][32][33], where in particular [33] establishes that for a general interacting field the KMS condition, and hence thermality, holds for accelerations above the mass scale. However, as with the Minkowski situation, the fact that the KMS condition holds for AdS does not specify the shape of the response spectrum for a particle detector in the spacetime.…”

Section: Introductionmentioning

confidence: 89%

1 V and Stable Dynamic Operation of Laser Diode Using Active Multi-Mode Interferometer

Shimizu

Razali

Kasahara

et al. 2005

Jpn. J. Appl. Phys.

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We consider the vacuum response of a particle detector in anti-de Sitter spacetime, and in particular analyze how spacetime features such as curvature and dimensionality affect the response spectrum of an accelerated detector. We calculate useful limits on Wightman functions, analyze the dynamics of the detector in terms of vacuum fluctuations and radiation reactions and discuss the thermalization process for the detector. We also discuss a generalization of the GEMS approach and obtain the Gibbons-Hawking temperature of de Sitter spacetime as an embedded Unruh temperature in a curved anti-de Sitter spacetime.

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“…In [2], [5] and [8] the authors show how the geometry of the de Sitter space-time and that of Anti-de-Sitter space-time, in particular the specific commutation relations in the corresponding symmetry groups, determine the value β for a β-KMS-state (see [11]) with respect to the dynamics given by a boost subgroup uniquely in each of the two space-times. Their results rely heavily on concrete calculations in the corresponding Lie algebras.…”

Section: β-Kms-statesmentioning

confidence: 99%

“…The arguments presented, as well as the idea of taking the assumption of passivity as a starting point of the investigation, were first published for the special case of Anti-de-Sitter space-time in [5] and [8].…”

Section: Invariance and Reeh-schlieder Propertymentioning

confidence: 99%

Passive states for essential observers

Strich

2008

Journal of Mathematical Physics

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The aim of this note is to present a unified approach to the results given in [2] and[8] which also covers examples of models not presented in these two papers (e.g. ddimensional Minkowski space-time for d ≥ 3). Assuming that a state is passive for an observer travelling along certain (essential) worldlines, we show that this state is invariant under the isometry group, is a KMS-state for the observer at a temperature uniquely determined by the structure constants of the Lie algebra involved and fulfills (a variant of) the Reeh-Schlieder property. Also the modular objects associated to such a state and the observable algebra of an observer are computed and a version of weak locality is examined.

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The second law of thermodynamics, TCP and Einstein causality in anti-de Sitter spacetime

Cited by 28 publications

References 10 publications

Thermal Aspects in Quantum Field Theory

Thermal Aspects in Quantum Field Theory

1 V and Stable Dynamic Operation of Laser Diode Using Active Multi-Mode Interferometer

Passive states for essential observers

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