On the algebra of test functions for field operators. Decomposition of linear functionals into positive ones

DOI10.1007/BF01646476zbMath0269.46031MaRDI QIDQ2563295

Jakob Yngvason

Publication date: 1973

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

Mathematics Subject Classification ID

Topological linear spaces of test functions, distributions and ultradistributions (46F05) Topological (rings and) algebras with an involution (46K99)

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On algebra \(\sharp\)-cones in topological tensor-algebras. I: Basic properties and normality ⋮ Algebras of unbounded operators in quantum field theory ⋮ On the cones of \(\alpha\) and generalized \(\alpha\)-positivity for quantum field theories with indefinite metric ⋮ On algebraic \(\sharp\)-cones in topological tensor algebras. II: Closed hulls and extremal rays ⋮ On quantum fields that generate local algebras ⋮ On topologization of unbounded operator algebras ⋮ Regular tensor algebras ⋮ Translationally invariant states and the spectrum ideal in the algebra of test functions for quantum fields ⋮ On the closed hull of subsets of inductive limits ⋮ Prime field decompositions and infinitely divisible states on Borcher's tensor algebra ⋮ Necessary and sufficient conditions for integral representations of Wightman functional at Schwinger points ⋮ Uniform topologies and strong operator topologies of polynomial algebras and on the algebra of CCR ⋮ The closure of cones in the algebra of test functions ⋮ Remarks on the reconstruction theorem for field theories with indefinite metric ⋮ Unnamed Item ⋮ New Methods in Conformal Partial Wave Analysis ⋮ Unnamed Item ⋮ On the existence of quantum fields in space-time dimension 4 ⋮ Graded and filtrated topological *-algebras. I: Graded normal topologies ⋮ On generally covariant mathematical formulation of Feynman integral in Lorentz signature ⋮ Unnamed Item ⋮ On the construction of fields and the topological role of Jacobi fields

Cites Work

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• On positive functionals on algebras of test functions for quantum fields
• The field algebra and its positive linear functionals
• Quantum Field Theory in Terms of Vacuum Expectation Values
• The Stieltjes moment problem for functions of bounded variation

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