KMS-like Properties of Local Thermal Equilibrium States in Quantum Field Theory

Michael Gransee, Nicola Pinamonti, and Rainer Verch

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Submission date: 30. Aug. 2015
Pages: 32
published in: Journal of geometry and physics, 117 (2017), p. 15-35 
DOI number (of the published article): 10.1016/j.geomphys.2017.02.014
Bibtex
Keywords and phrases: local thermal equilibrium, Quantum Field Theory, KMS condition, Quantum Statistical Mechanics
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Abstract:
A new condition, called “Local KMS Condition”, characterizing states of a quantum field to which one can ascribe, at a given spacetime point, a temperature, is introduced in this article. It will be shown that the Local KMS Condition (LKMS condition) is equivalent to the Local Thermal Equilibrium (LTE) condition, proposed previously by Buchholz, Ojima and Roos, for states of the quantized scalar Klein-Gordon field that fulfill the analytic microlocal spectrum condition. Therefore, known examples of states fulfilling the LTE condition provide examples of states obeying the LKMS condition with a temperature distribution varying in space and time. The results extend to the generalized cases of mixed-temperature LKMS and LTE states. The LKMS condition therefore provides a promising generalization of the KMS condition, which characterizes global thermal equilibrium states with respect to an inertial time evolution, to states which are globally out of equilibrium but still possess a local temperature distribution.