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

DOI10.1016/0003-4916(89)90075-4zbMath0662.60116OpenAlexW2019240833MaRDI QIDQ1113558

Roman Gielerak

Publication date: 1989

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0003-4916(89)90075-4

zbMATH Keywords

Euclidean quantum field theoryDobrushin-Lanford-Ruelle equationinfinite volume free energy densititiesLee- Yang theorem

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic mechanics (including stochastic electrodynamics) (81P20)

Related Items (2)

Vacuum energy densities in the \({\mathcal J} (\Phi{})_ 2\) Euclidean field theory ⋮ Euclidean Gibbs measures of interacting quantum anharmonic oscillators

Cites Work

• Uniqueness and the global Markov property for Euclidean fields: The case of general exponential interaction
• The Gibbs measures and partial differential equations. I. Ideas and local aspects
• Vacuum energy density in \({\mathcal P}(\phi)_ 2\) theories. Independence of (non-classical) boundary conditions (modified version)
• Uniqueness and the global Markov property for Euclidean fields. The case of trigonometric interactions
• Elliptic equations and Gaussian processes
• Seminaire de probabilites IX. Universite de Strasbourg. Edited by P. A. Meyer
• Specifications and Martin boundaries for \(\mathcal P(\phi)_2\)-random fields
• The free Markoff field
• Analytic and clustering properties of thermodynamic functions and distribution functions for classical lattice and continuum systems
• Construction of quantum fields from Markoff fields
• Representation of States in a Field Theory with Canonical Variables
• Hamiltonian Formalism and the Canonical Commutation Relations in Quantum Field Theory
• On the DLR equation for the two-dimensional sine–Gordon model
• The D.L.R. conditions for translation invariant Gaussian measures on L(R d)
• A note on specifications
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