Construction of KMS States in Perturbative QFT and Renormalized Hamiltonian Dynamics

Klaus Fredenhagen, Falk Lindner
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