Measures on Schwartz distribution space and applications to \(P(\varphi)_2\) field theories

DOI10.1016/S0001-8708(74)80018-6zbMath0313.28015MaRDI QIDQ1220163

James G. Glimm, Jonathan Dimock

Publication date: 1974

Published in: Advances in Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) (46G99)

Related Items (18)

The loop expansion for the effective potential in the \(P(\Phi)_ 2\) quantum field theory ⋮ On dimensional reduction of functional measures ⋮ Uniqueness and global Markov property for Euclidean fields: The case of general polynomial interactions ⋮ Probabilistic aspects of quantum field theory ⋮ Uniqueness of Gibbs states for general \(P(\phi)_ 2\)-weak coupling models by cluster expansion ⋮ Legendre transforms and r-particle irreducibility in quantum field theory: the formal power series framework ⋮ Cluster expansion for P(φ)2: explicit estimates ⋮ AdS/CFT correspondence in the Euclidean context ⋮ Axioms for Euclidean Green's functions ⋮ Continuous sample paths in quantum field theory ⋮ The Wilson loop observables of Chern-Simons theory on \({\mathbb{R}}^3\) in axial gauge ⋮ Schwinger functions and their generating functionals. II. Markovian and generalized path space measures on \(\mathcal S'\) ⋮ The Glimm-Jaffe-Spencer expansion for the classical boundary conditions and coexistence of phases in the \(\lambda\varphi^4_2\) Euclidean (quantum) field theory ⋮ Phase transitions in a continuous three states model with discrete gauge symmetry ⋮ REMARK ON THE INTEGRATION BY PARTS FORMULA FOR THE $\phi_3^4$-QUANTUM FIELD MODEL ⋮ A cluster expansion for stochastic lattice fields ⋮ Support properties of the free measure for boson fields ⋮ On the stochastic quantization of field theory

Cites Work

• Unnamed Item
• The construction of stationary two-dimensional Markoff fields with an application to quantum field theory
• Nonlinear functions of weak processes. I
• The \(\lambda (\varphi^ 4)_ 2\) quantum field theory without cutoffs. II: The field operators and the approximate vacuum
• Small distance behaviour in field theory and power counting
• Positivity and self adjointness of the \(P(\phi)_ 2\) Hamiltonian
• Construction of quantum fields from Markoff fields
• Rigorous quantum field theory models
• Stationary Stochastic Processes. (MN-8)

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