Necessary and sufficient conditions for integral representations of Wightman functional at Schwinger points

DOI10.1007/BF01609839zbMath0319.46060MaRDI QIDQ1222845

Jakob Yngvason, Hans-Jürgen Borchers

Publication date: 1976

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

Mathematics Subject Classification ID

Applications of functional analysis in quantum physics (46N50) Operator algebra methods applied to problems in quantum theory (81R15) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) (46G99)

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Algebras of unbounded operators in quantum field theory ⋮ Unnamed Item ⋮ Uniform topologies on enveloping algebras ⋮ CONVOLUTED GENERALIZED WHITE NOISE, SCHWINGER FUNCTIONS AND THEIR ANALYTIC CONTINUATION TO WIGHTMAN FUNCTIONS ⋮ Euclidean random fields obtained by convolution from generalized white noise ⋮ Symmetric tensor algebras and integral decompositions ⋮ A nuclear Weyl algebra ⋮ Translationally invariant states and the spectrum ideal in the algebra of test functions for quantum fields ⋮ On revolutionizing quantum field theory with Tomita’s modular theory ⋮ Complex classical fields: a framework for reflection positivity ⋮ On Inner Characterizations of Aõ-Algebras and some Applications to Calkin Algebras and Symmetric Tensor-Algebras ⋮ Stochastically positive structures on Weyl algebras. The case of quasi-free states ⋮ Hamiltonian renormalisation I: derivation from Osterwalder–Schrader reconstruction ⋮ Hamiltonian renormalization III. Renormalisation flow of 1  +  1 dimensional free scalar fields: properties ⋮ On the decomposition of Wightman functionals in the Euclidean framework ⋮ On the symmetrized cones in test function algebra ⋮ Canonical quantization of lattice Higgs–Maxwell–Chern–Simons fields: Osterwalder–Schrader positivity ⋮ Graded and filtrated topological *-algebras. I: Graded normal topologies ⋮ Unnamed Item

Cites Work

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• On local field products in special Wightman theories
• Axioms for Euclidean Green's functions. II
• Integral representations for Schwinger functionals and the moment problem over nuclear spaces
• Extremal decomposition of Wightman functions and of states on nuclear \(^*\)-algebras by Choquet theory
• Euclidean field theory. I: The moment problem
• Axioms for Euclidean Green's functions
• Remarks concerning the connection between properties of the 4-point-function and the Wilson-Zimmermann expansion
• The field algebra and its positive linear functionals
• Topological algebras of operators
• On the algebra of test functions for field operators. Decomposition of linear functionals into positive ones
• The Stieltjes moment problem for functions of bounded variation

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