On a class of equilibrium states under the Kubo-Martin-Schwinger condition

Rocca, F.; Sirugue, M.; Testard, D.

doi:10.1007/bf01646630

Cited by 43 publications

(30 citation statements)

References 8 publications

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“…dp{x) = j (P dpj(p). we get a result, which is a slight generalization of one in [4] and analogous to one in [18], [8]. …”

Section: The Central Decomposition Of Gauge-invariant Quasi-free Statessupporting

confidence: 64%

Decomposition of Positive Sesquilinear Forms and the Central Decomposition of Gauge-Invariant Quasi-Free States on the Weyl-Algebra

Honegger

1990

Zeitschrift Für Naturforschung A

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A decomposition theory for positive sesquilinear forms densely defined in Hilbert spaces is developed. On decomposing such a form into its closable and singular part and using Bochner's theorem it is possible to derive the central decomposition of the associated gauge-invariant quasifree state on the boson C*-Weyl algebra. The appearance of a classical field part of the boson system is studied in detail in the GNS-representation and shown to correspond to the so-called singular subspace of a natural enlargement of the one-boson testfunction space. In the example of Bose-Einstein condensation a non-trivial central decomposition (or equivalently a non-trivial classical field part) is directly related to the occurrence of the condensation phenomenon.

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“…dp{x) = j (P dpj(p). we get a result, which is a slight generalization of one in [4] and analogous to one in [18], [8]. …”

Section: The Central Decomposition Of Gauge-invariant Quasi-free Statessupporting

confidence: 64%

Decomposition of Positive Sesquilinear Forms and the Central Decomposition of Gauge-Invariant Quasi-Free States on the Weyl-Algebra

Honegger

1990

Zeitschrift Für Naturforschung A

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“…Following [25] we replace all V i in this condition by 1 N N −1 k=0 T k x V i and take the limit N → ∞. Then by (6.7), Lemma 5.1(vi), and the ergodic theorem one has β i β k f (V k − V i ) ≥ 0, hence f is of positive type (the remaining conditions, f (0) = 1 and f (V ) = f (−V ), are obviously satisfied).…”

Section: Vacuum Versus Regular Positive Energy Representationsmentioning

confidence: 99%

Semidirect product of CCR and CAR algebras and asymptotic states in quantum electrodynamics

Herdegen

1998

Journal of Mathematical Physics

101

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A C * -algebra containing the CCR and CAR algebras as its subalgebras and naturally described as the semidirect product of these algebras is discussed. A particular example of this structure is considered as a model for the algebra of asymptotic fields in quantum electrodynamics, in which Gauss' law is respected. The appearence in this algebra of a phase variable related to electromagnetic potential leads to the universal charge quantization. Translationally covariant representations of this algebra with energy-momentum spectrum in the future lightcone are investigated. It is shown that vacuum representations are necessarily nonregular with respect to total electromagnetic field. However, a class of translationally covariant, irreducible representations is constructed excplicitly, which remain as close as possible to the vacuum, but are regular at the same time. The spectrum of energy-momentum fills the whole future lightcone, but there are no vectors with energy-momentum lying on a mass hyperboloid or in the origin. *

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“…As a starting point for further development, we analyse in details the case of quasi-free states (Section III). Although basic structural results characterizing quasi-free thermal states have been obtained long time ago [28,29,30], we present new (in our opinion simpler) proof of the theorem giving general form of a quasi-free state satisfying the KMS condition (see Theorem 3.1 and 3.7). Section 3.4 contains complete characterizations of stochastically positive quasi-free KMS states and corresponding periodic stochastic processes.…”

Section: Introductionmentioning

confidence: 90%

Stochastically positive structures on Weyl algebras. The case of quasi-free states

Gielerak

Jakóbczyk

Olkiewicz

1998

Journal of Mathematical Physics

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We consider quasi-free stochastically positive ground and thermal states on Weyl algebras in Euclidean time formulation. In particular, we obtain a new derivation of a general form of thermal quasi-free state and give conditions when such state is stochastically positive i.e. when it defines periodic stochastic process with respect to Euclidean time, so called thermal process. Then we show that thermal process completely determines modular structure canonically associated with quasifree thermal state on Weyl algebra. We discuss a variety of examples connected with free quantum field theories on globally hyperbolic stationary space-times and models of quantum statistical mechanics.

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On a class of equilibrium states under the Kubo-Martin-Schwinger condition

Cited by 43 publications

References 8 publications

Decomposition of Positive Sesquilinear Forms and the Central Decomposition of Gauge-Invariant Quasi-Free States on the Weyl-Algebra

Decomposition of Positive Sesquilinear Forms and the Central Decomposition of Gauge-Invariant Quasi-Free States on the Weyl-Algebra

Semidirect product of CCR and CAR algebras and asymptotic states in quantum electrodynamics

Stochastically positive structures on Weyl algebras. The case of quasi-free states

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