Uniqueness and global Markov property for Euclidean fields: The case of general polynomial interactions

DOI10.1007/BF01238808zbMath0668.60093OpenAlexW2028693397MaRDI QIDQ1118271

Sergio A. Albeverio, Raphael J. Høegh-Krohn, Bogusław Zegarliński

Publication date: 1989

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01238808

zbMATH Keywords

extremality of Gibbs statesglobal Markov property for Euclidean quantum fields

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic mechanics (including stochastic electrodynamics) (81P20) Markov processes (60J99)

Related Items

Along Paths Inspired by Ludwig Streit: Stochastic Equations for Quantum Fields and Related Systems, Bounded perturbations of the generalized random fields, Ergodicity for the stochastic dynamics of quasi-invariant measures with applications to Gibbs states, Non-local Markovian symmetric forms on infinite dimensional spaces. II: Applications: non local stochastic quantization of space cut-off quantum fields and infinite particle systems, CONVOLUTED GENERALIZED WHITE NOISE, SCHWINGER FUNCTIONS AND THEIR ANALYTIC CONTINUATION TO WIGHTMAN FUNCTIONS, Uniqueness of Gibbs states for general \(P(\phi)_ 2\)-weak coupling models by cluster expansion, Euclidean random fields obtained by convolution from generalized white noise, Random fields as solutions of the inhomogeneous quaternionic Cauchy- Riemann equation. I: Invariance and analytic continuation, Dobrushin uniqueness theorem and logarithmic Sobolev inequalities, Non-local Markovian symmetric forms on infinite dimensional spaces. I: The closability and quasi-regularity, Vacuum energy densities in the \({\mathcal J} (\Phi{})_ 2\) Euclidean field theory, \(H\)-\(C^1\) maps and elliptic SPDEs with polynomial and exponential perturbations of Nelson's Euclidean free field

Cites Work

• On Dynkin's Markov property of random fields associated with symmetric processes
• The construction of stationary two-dimensional Markoff fields with an application to quantum field theory
• Uniqueness of Gibbs states for general \(P(\phi)_ 2\)-weak coupling models by cluster expansion
• Markov property of generalized fields and axiomatic potential theory
• Local and global Markoff fields
• Uniqueness and the global Markov property for Euclidean fields: The case of general exponential interaction
• Uniqueness of Gibbs fields via cluster expansions
• On the Markov property for certain Gaussian random fields
• Examples of extremal lattice fields without the global Markov property
• Some examples concerning the global Markov property
• The Gibbs measures and partial differential equations. I. Ideas and local aspects
• On the uniqueness of Markovian self-adjoint extension of diffusion operators on infinite dimensional spaces
• Attractiveness of interactions for binary lattice systems and the global Markov property
• Extremality and the global Markov property II: The global Markov property for non-FKG maximal Gibbs measures
• Remarks on the global Markov property
• Local perturbations of conditional expectations
• Uniqueness and the global Markov property for Euclidean fields. The case of trigonometric interactions
• Convergence to equilibrium of the stochastic Heisenberg model
• Compactness and the maximal Gibbs state for random Gibbs fields on a lattice
• The global Markov property for lattice systems
• Gibbs measures and phase transitions
• Construction of a one-dimensional quantum field by means of a continuous Markov field
• On the equivalence of the Euclidean and Wightman formulation of field theory
• Axioms for Euclidean Green's functions. II
• Some aspects of Markov and Euclidean field theories
• Measures on Schwartz distribution space and applications to \(P(\varphi)_2\) field theories
• On the germ fields of stationary Gaussian processes with Markovian property
• Random fields
• Schwinger functions and their generating functionals. II. Markovian and generalized path space measures on \(\mathcal S'\)
• Correlation inequalities on some partially ordered sets
• Étude des champs euclidiens sur un réseau \(\mathbb{Z}^nu\)
• The Glimm-Jaffe-Spencer expansion for the classical boundary conditions and coexistence of phases in the \(\lambda\varphi^4_2\) Euclidean (quantum) field theory
• A Markov property for Gaussian processes with a multidimensional parameter
• Specifications and Martin boundaries for \(\mathcal P(\phi)_2\)-random fields
• Some central limit theorems for Markov paths and some properties of Gaussian random fields
• Extremality and the global Markov property. I: The Euclidean fields on a lattice
• Generalized Brownian functionals and the solution to a stochastic partial differential equation
• The Wightman axioms and the mass gap for strong interactions of exponential type in two-dimensional space-time
• Analytic vectors for representations of the canonical commutation relations and nondegeneracy of ground states
• The free Markoff field
• Axioms for Euclidean Green's functions
• From Euclidean to relativistic fields and on the notion of Markoff fields
• The problem of uniqueness of a Gibbsian random field and the problem of phase transitions
• 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
• Markov processes and random fields
• 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)
• Dirichlet forms and diffusion processes on rigged Hilbert spaces
• Gaussian OS-positive processes
• Limit theorems for sums of dependent random variables occurring in statistical mechanics
• Existence and uniqueness of DLR measures for unbounded spin systems
• On notions of Markov property
• Markov systems of imprimitivity
• Martin-Dynkin boundary of mixed poisson processes
• On quantum theory in terms of white noise
• Processus gaussiens, equivalence d'ensembles et specification locale
• Necessary and Sufficient Conditions for the GHS Inequality with Applications to Analysis and Probability
• A Dirichlet problem for distributions and specifications for random fields
• Homogeneous Gauss-Markov Random Fields
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item