# Construction of KMS States in Perturbative QFT and Renormalized Hamiltonian Dynamics

June 28, 2013

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 finite 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.

open access link
Communications in Mathematical Physics Volume 332, Issue 3, pp
895-932, 2014-12-01

@article{Fredenhagen:2013cna,
author = "Fredenhagen, Klaus and Lindner, Falk",
title = "{Construction of KMS States in Perturbative QFT and
Renormalized Hamiltonian Dynamics}",
journal = "Commun. Math. Phys.",
volume = "332",
year = "2014",
number = "3",
pages = "895-932",
doi = "10.1007/s00220-014-2141-7, 10.1007/s00220-016-2725-5",
note = "[Erratum: Commun. Math. Phys.347,no.2,655(2016)]",
eprint = "1306.6519",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1306.6519;%%"
}

Keywords:

KMS states, perturbative AQFT, causal perturbation theory, thermal quantum field theory