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Towards a Relativistic KMS Condition

Jacques Bros A, Service de Physique Theorique, Detlev Buchholz A

Published Jul 15, 1998• 65 citations
OpenAlex

Abstract

It is shown that, under quite general conditions, thermal correlation functions in relativistic quantum field theory have stronger analyticity properties in configuration space than those imposed by the KMS-condition. These analyticity properties may be understood as a remnant of the relativistic spectrum condition in the vacuum sector and lead to a Lorentz-covariant formulation of the KMS-condition involving all space-time variables. 1

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It is shown that, under quite general conditions, thermal correlation functions in relativistic quantum field theory have stronger analyticity properties in configuration space than those imposed by the KMS-condition. These analyticity properties may be understood as a remnant of the relativistic spectrum condition in the vacuum sector and lead to a Lorentz-covariant formulation of the KMS-condition involving all space-time variables. 1
This work investigates structural constraints imposed by analyticity in relativistic quantum field theory on classical causal explanations of quantum correlations. Building on previous results on analytic rigidity, we establish a conditional obstruction to the realization of classical causal factorizations through spacetime-localized modifications of two-point correlation functions. The argument derives analyticity directly from the spectral condition and identifies clustering as the key mechanism linking probabilistic factorization with analytic constraints. We then extend the analysis to three-point functions. A marginal spectral condition is introduced as a natural generalization compatible with dimensional reduction. Under this framework, we prove that any admissible modification must vanish upon reduction to all two-point marginals. The irreducible three-point sector is analyzed via connected correlation functions. A conditional obstruction is obtained under an extended analytic rigidity hypothesis in higher-dimensional tube domains, which is formulated explicitly as an open problem. The work provides a unified perspective connecting analytic properties of quantum field theory with causal modeling approaches to quantum correlations, and outlines a program for extending these results to higher-point functions.
The author shows that properties like spectrum condition, analyticity of n-point functions, space-like clustering of correlation functions stronger than any inverse power, the Reeh-Schlieder property do hold in Galilei invariant quantum theory. Furthermore, the range of validity of Haag's theorem is briefly discussed. The results seems to be of relevance both in the non-relativistic regime proper and as a hint that many of the properties typically attributed to relativistic field theories are actually a common feature of every theory with a zero mean-particle density and translation-invariant Hamiltonian.