Construction of KMS States in Perturbative QFT and Renormalized Hamiltonian Dynamics

TL;DR

This paper develops a method to construct KMS states in perturbative algebraic quantum field theory, extending the Schwinger-Keldysh formalism, and addresses infrared divergences by leveraging locality properties.

Contribution

It introduces a Hamiltonian framework for interacting dynamics in pAQFT, providing a rigorous link between relativistic QFT and quantum statistical mechanics.

Findings

Successfully constructs KMS states in pAQFT at positive temperature.

Shows infrared divergences are absent due to locality properties.

Provides a Hamiltonian description connecting QFT and statistical mechanics.

Abstract

We present a general construction of KMS states in the framework of perturbative algebraic quantum field theory (pAQFT). Our approach may be understood as an extension of the Schwinger-Keldysh formalism. We obtain in particular the Wightman functions at positive temperature, thus solving a problem posed some time ago by Steinmann. The notorious infrared divergences observed in a diagrammatic expansion are shown to be absent due to a consequent exploitation of the locality properties of pAQFT. To this avail, we introduce a novel, Hamiltonian description of the interacting dynamics and find, in particular, a precise relation between relativistic QFT and rigorous quantum statistical mechanics.