Journal ArticleDOI
On the equilibrium states in quantum statistical mechanics
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In this article, the authors studied the representation of the C*-algebra of observables corresponding to thermal equilibrium of a system at given temperature T and chemical potential μ and showed that the representation is reducible and that there exists a conjugation in the representation space, which maps the von Neumann algebra spanned by the representative of\(\mathfrak{A}\) onto its commutant.Abstract:
Representations of theC*-algebra\(\mathfrak{A}\) of observables corresponding to thermal equilibrium of a system at given temperatureT and chemical potential μ are studied. Both for finite and for infinite systems it is shown that the representation is reducible and that there exists a conjugation in the representation space, which maps the von Neumann algebra spanned by the representative of\(\mathfrak{A}\) onto its commutant. This means that there is an equivalent anti-linear representation of\(\mathfrak{A}\) in the commutant. The relation of these properties with the Kubo-Martin-Schwinger boundary condition is discussed.read more
Citations
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General properties of entropy
TL;DR: This paper discusses properties of entropy, as well as related concepts such as relative entropy, skew entropy, dynamical entropy, etc, in detail with reference to their implications in statistical mechanics, to get a glimpse of systems with infinitely many degrees of freedom.
Journal ArticleDOI
The Unruh effect and its applications
TL;DR: The Unruh effect has played a crucial role in our understanding that the particle content of a field theory is observer dependent as mentioned in this paper, which is important in its own right and as a way to understand the phenomenon of particle emission from black holes and cosmological horizons.
Journal ArticleDOI
Theorems on the uniqueness and thermal properties of stationary, nonsingular, quasifree states on spacetimes with a bifurcate killing horizon
Bernard S. Kay,Robert M. Wald +1 more
TL;DR: In this article, the authors studied the properties of quasifree states of a linear, scalar quantum field in globally hyperbolic spacetimes possessing a one-parameter group of isometries with a bifurcate Killing horizon.
Book
Operator Algebras: Theory of C*-Algebras and von Neumann Algebras
TL;DR: In this article, the authors present a model for operators on Hilbert Space, including C*-Algebras, Von Neumann Algebra, and K-Theory and Finiteness.
Journal ArticleDOI
On the duality condition for a Hermitian scalar field
TL;DR: In this paper, a general Hermitian scalar field, assumed to be an operator−valued tempered distribution, is considered and a theorem which relates certain complex Lorentz transformations to the TCP transformation is stated and proved.
References
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Statistical-Mechanical Theory of Irreversible Processes : I. General Theory and Simple Applications to Magnetic and Conduction Problems
TL;DR: In this paper, a general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of timefluctuation of dynamical variables associated with such irreversible processes.
Journal ArticleDOI
Theory of Many-Particle Systems. I
Paul C. Martin,Julian Schwinger +1 more
TL;DR: In this paper, a series of papers dealing with many-particle systems from a unified, nonperturbative point of view is presented, which includes derivations and discussions of various field-theoretical techniques which will be applied in subsequent papers.
Journal ArticleDOI
Representations of the canonical commutation relations describing a nonrelativistic infinite free bose gas
H. Araki,E. J. Woods +1 more
TL;DR: The existence of inequivalent representations of the canonical commutation relations which describe a nonrelativistic infinite free Bose gas of uniform density is investigated in this article, with a view to possible applications to statistical mechanics.
Journal ArticleDOI
Covariance algebras in field theory and statistical mechanics
TL;DR: In this paper, a covariance algebra is constructed for relativistic field theory with the property that the corresponding *-representations are in one-to-one correspondence with covariant representations of the automorphisms.