# The Relation Between KMS States For Different Temperatures

C. Jaekel

Published 1998 · Physics, Mathematics

Abstract.
Given a thermal field theory for some temperature
$$ \beta^-1 $$
, we construct
the theory at an arbitrary temperature
$$ 1/\beta' $$
. Our work is based on a construction
invented by Buchholz and Junglas, which we adapt to thermal field theories. In
a first step we construct states which closely resemble KMS states for the new
temperature in a local region
$$ \mathcal O_{\circ} \subset \mathbb{R}^4 $$
, but coincide with the given KMS state in
the space-like complement of a slightly larger region
Ô. By a weak*-compactness
argument there always exists a convergent subnet of states as the size of
$$ \mathcal O_{\circ} $$
and Ô tends towards
$$ \mathbb{R}^4 $$
. Whether or not such a limit state is a global KMS state for the
new temperature, depends on the surface energy contained in the layer in between
the boundaries of
$$ \mathcal O_{\circ} $$
and Ô. We show that this surface energy can be controlled
by a generalized cluster condition.

This paper references

10.1090/s0002-9904-1965-11247-2

Review: R. F. Streater and A. S. Wightman, PCT, Spin and statistics, and all that

D. Ruelle (1965)

10.2140/pjm.1974.50.309

Some properties of modular conjugation operator of von Neumann algebras and a non-commutative Radon-Nikodym theorem with a chain rule.

H. Araki (1974)

Springer-Verlag Berlin-Heidelberg-New York

E. Zwicker (1998)

Real - and imaginarytime field theory at finite temperature and density

N. P. LvW Landsman (1987)

10.1016/0022-1236(90)90104-S

Nuclear maps and modular structures. I. General properties

D. Buchholz (1990)

Algebraic properties of thermal field theories, ESI-preprint, in preparation

C D Jä B ] Jäkel

10.1016/0370-1573(87)90121-9

Real- and imaginary-time field theory at finite temperature and density

N. P. Landsman (1987)

10.1007/BF00417464

Local properties of equilibrium states and the particle spectrum in quantum field theory

D. Buchholz (1986)

Thermodynamisches Gleichgewicht und Energiespektrum in der Quantenfeldtheorie

P. Junglas (1987)

10.1103/PhysRev.115.1342

Theory of Many-Particle Systems. I

P. Martin (1959)

Algebraic properties of thermal quantum field theories, in preparation

C D Jä B ] Jäkel

On the uniqeness of the equilibrium state for an interacting fermion gas at high temperatures and low densities , Lett

C. D. Jäkel (1995)

Theory of Many-Particle Systems

I. P. Bazarov (1989)

10.1016/c2009-0-19635-6

Fundamentals of the Theory of Operator Algebras

R. Kadison (1983)

Finite Temperautre Field Theory

J I Kapusta (1989)

The relation between KMS-states for different temperatures [Jä b] Jäkel, C.D., On the relation between KMS states for different temperatures

10.1007/978-3-7091-7526-2

A Course in Mathematical Physics

W. Thirring (1978)

Statistical Mechanics: Rigorous Results

D. Ruelle (1999)

10.1007/3-540-54978-1_14

Nonexistence of scattering theory at finite temperature

H. Narnhofer (1991)

10.1007/BF00703730

Generalized nuclearity conditions and the split property in quantum field theory

D. Buchholz (1991)

10.1007/BF01645628

Remarks on spectra of modular operators of von Neumann algebras

H. Araki (1972)

On the hadronic mass spectrum, Nuovo Cim

R Hagedorn (1967)

10.1080/00927878908823824

Algebras and their automorphism groups

R. D. Pollack (1989)

10.1143/JPSJ.12.570

Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems

R. Kubo (1957)

C*-Algebras and Their Automorphisms Groups, Academic Press, London-New YorkTokyo

G. K. Pedersen (1979)

10.1063/1.533089

Two algebraic properties of thermal quantum field theories

C. Jäkel (1999)

10.1103/PhysRevA.26.3646

Adiabatic theorem in quantum statistical mechanics

H. Narnhofer (1982)

10.1007/BF02108335

Perturbative quantum field theory at positive temperatures: An axiomatic approach

O. Steinmann (1995)

10.1142/2364

Thermal field theory

M. Bellac (1996)

10.1007/BF01239029

Convergence of local charges and continuity properties ofW*-inclusions

C. d'Antoni (1987)

10.1142/S0129055X92000145

FROM QUANTUM FIELDS TO LOCAL VON NEUMANN ALGEBRAS

H. Borchers (1992)

Nuclearity and split for thermal quantum field theories

C. Jäkel (1998)

Local Quantum Physics: Fields, Particles, Algebras

R. Haag (1992)

10.1007/BF02096782

Nuclear maps and modular structures II: Applications to quantum field theory

D. Buchholz (1990)

10.1007/BF00398332

Asymptotic triviality of the Møller operators in Galilei invariant quantum field theories

C. Jaekel (1991)

10.1007/978-3-662-09089-3

Operator algebras and quantum statistical mechanics

Ola Bratteli (1979)

Decay of Spatial Correlations in Thermal States

C. Jäkel (1998)

10.1007/BF00750814

On the uniqueness of the equilibrium state for an interacting fermion gas at high temperatures and low densities

C. Jaekel (1995)

10.1007/BF00047144

Quantum theory of collective phenomena

S. Panfil (1991)

10.1007/BF01565114

Particles and propagators in relativistic thermo field theory

J. Bros (1992)

10.1515/9781400884230

PCT, spin and statistics, and all that

R. F. Streater (1964)

Relativistic KMS-condition and Kaellen-Lehmann type representatios of thermal propagators

J. Bros (1995)

The Reeh–Schlieder property for thermal states

C D Jäkel (2000)

10.1142/S0129055X94000390

ENTROPY DENSITY FOR RELATIVISTIC QUANTUM FIELD THEORY

H. Narnhofer (1994)

10.1063/1.1704187

An Algebraic Approach to Quantum Field Theory

R. Haag (1964)

10.1007/BF01609344

Spectra of Liouville operators

G. T. Brinke (1976)

10.1007/BF01651541

Stability and equilibrium states

R. Haag (1974)

10.1007/BF01649582

Disjointness of the KMS-states of different temperatures

M. Takesaki (1970)

10.1007/978-3-642-87665-3

Nuclear Locally Convex Spaces

A. Pietsch (1972)

10.1007/BF01646342

On the equilibrium states in quantum statistical mechanics

R. Haag (1967)

10.1007/978-3-319-17545-4_20

On the Hadronic Mass Spectrum

R. Hagedorn (1967)

10.1007/BF01388641

Standard and split inclusions of von Neumann algebras

S. Doplicher (1984)

10.1007/BF01454978

Causal independence and the energy-level density of states in local quantum field theory

D. Buchholz (1986)

10.1063/1.1704063

Von Neumann Algebras of Local Observables for Free Scalar Field

H. Araki (1964)

Cluster properties for modular structures, ESI-preprint, in preparation

C D Jä C ] Jäkel

Thermal Field Theory, Cambridge University

M. Le Bellac (1996)

10.1007/BF01217805

On the existence of equilibrium states in local quantum field theory

D. Buchholz (1989)

Axiomatic analyticity properties and representations of particles in thermal quantum field theory

J. Bros (1996)

Thermodynamisches Gleichgewicht und Energiespektrum in der Quantenfeldtheorie , Dissertation

P Junglas (1987)

10.1016/0550-3213(94)00298-3

Towards a relativistic KMS-condition

J. Bros (1994)

10.1063/1.533208

The Reeh–Schlieder property for thermal field theories

C. Jäkel (2000)

Cluster estimates for modular structures, hep-th/9804017

C D Jä C ] Jäkel

Finite Temperautre Field

J. I. Kapusta (1989)

Ch.G., Real- and imaginary-time field theory at finite temperature and density

N. P. LvW Landsman (1987)

Relativistic KMS-condition and Källén-Lehmann type representation of thermal propagators, published in Proceedings of the 4th Workshop on Thermal Field Theories and their Applications

J. Bros (1995)

10.1017/CBO9780511662218

Operator algebras in dynamical systems

S. Sakai (1991)

10.1016/c2016-0-03431-9

C-Algebras and Their Automorphism Groups

G. K. Pedersen (1979)

Algebraic methods in statistical mechanics and quantum field theory

G. G. Emch (1972)

Some properties of modular conjugation operator of a von Neumann algebra and a noncommutative Radon-Nikodym theorem with a chain rule From quantum fields to local von Neumann algebras

H Araki (1974)

Finite Temperature Field Theory, Cambridge University

J. I. Ka Kapusta (1989)

Advanced Field Theory

H. Umezawa (1995)

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