On the DLR equation for the \((\lambda:\phi^ 4: +b:\phi^ 2:+\mu\phi\), \(\mu\neq 0)_ 2\) Euclidean quantum field theory: The uniqueness theorem
type: Item
instance of: scholarly article
title: On the DLR equation for the \((\lambda:\phi^ 4: +b:\phi^ 2:+\mu\phi\), \(\mu\neq 0)_ 2\) Euclidean quantum field theory: The uniqueness theorem
zbMATH Open document ID: 0662.60116
DOI: 10.1016/0003-4916(89)90075-4
author: Roman Gielerak
published in: Annals of Physics
publication date: 1989-01-01T00:00:00Z
review text: The Dobrushin-Lanford-Ruelle (DLR) equation is studied in a certain space of measures in the case of 2-dimensional \(\lambda:\phi^ 4:+b:\phi^ 2:+\mu \phi\), \(\mu\neq 0\), Euclidean quantum field theory. The uniqueness theorem stating that for any \(\mu\neq 0\) there exists unique, translationally invariant 8-regular solutions of the corresponding DLR equation is proved. The theorem is proved by combining the Lee-Yang theorem with the general van Hove type theorem for infinite volume free energy densitities.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 81P20
zbMATH DE Number: 4082694
zbMATH Keywords: Dobrushin-Lanford-Ruelle equation
zbMATH Keywords: Euclidean quantum field theory
zbMATH Keywords: Lee- Yang theorem
zbMATH Keywords: infinite volume free energy densitities
MaRDI profile type: Publication
full work available at URL: 0003-4916(89)90075-4
OpenAlex ID: W2019240833
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description: scientific article; zbMATH DE number 4082694