The semigroup characterization of Osterwalder-Schrader path spaces and the construction of Euclidean fields

DOI10.1016/0022-1236(78)90009-5zbMath0382.46030OpenAlexW2076568617MaRDI QIDQ1248099

Abel Klein

Publication date: 1978

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(78)90009-5

Mathematics Subject Classification ID

General groups of measure-preserving transformations (28D15) Axiomatic quantum field theory; operator algebras (81T05) Miscellaneous applications of functional analysis (46N99) One-parameter continuous families of measure-preserving transformations (28D10)

Related Items

THERMAL QUANTUM FIELDS WITHOUT CUT-OFFS IN 1+1 SPACE-TIME DIMENSIONS, Uniqueness and the global Markov property for Euclidean fields. The case of trigonometric interactions, Construction of a unique self-adjoint generator for a symmetric local semigroup, Stochastic processes associated with KMS states, Reflection positivity and conformal symmetry, A characterization of Osterwalder-Schrader path spaces by the associated semigroup, Gaussian OS-positive processes, Thermal quantum fields with spatially cutoff interactions in 1+1 space--time dimensions, Reflection positive stochastic processes indexed by Lie groups, Markov operators and OS-positive processes, From the Euclidean group to the Poincaré group via Osterwalder-Schrader positivity, Infinitely divisible OS-positive processes, Reflection positive one-parameter groups and dilations

Cites Work

• Axioms for Euclidean Green's functions. II
• Constructive quantum field theory. The 1973 'Ettore Majorana' international school of mathematical physics
• Singular perturbations of positivity preserving semigroups via path space techniques
• The free Markoff field
• Small distance behaviour in field theory and power counting
• Time-ordered operator products of sharp-time quadratic forms
• Construction of quantum fields from Markoff fields
• A characterization of Osterwalder-Schrader path spaces by the associated semigroup
• The λφ24 Quantum Field Theory without Cutoffs. IV. Perturbations of the Hamiltonian
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