On field algebras in quantum theory with indefinite metric

DOI10.1007/BF01017122zbMath0536.47035OpenAlexW2057199062MaRDI QIDQ791858

K. Yu. Dadashyan, S. S. Khoruzhij

Publication date: 1983

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01017122

zbMATH Keywords

Krein spacelocal commutativityquantum gauge theory\(WJ^*\)-algebras of bounded operatorsBisognano-Wichmann formalismOp \(J^*\)-algebrapolynomial algebra of unbounded operatorsquantum field theory in the state space with indefinite metricrelativistic covarianceresolvent of J-positive operators

Mathematics Subject Classification ID

Applications of operator algebras to the sciences (47L90) Axiomatic quantum field theory; operator algebras (81T05) Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Miscellaneous applications of functional analysis (46N99)

Related Items (9)

Unnamed Item ⋮ Some algebras of unbounded operators in an indefinite inner product vector space ⋮ Irreducibility and reducing subspaces for Krein space representations of field algebra ⋮ Unbounded GNS representations of a *-algebra in a Krein space ⋮ Quasivectors and Tomita–Takesaki Theory for Operator Algebras on Π₁-Spaces ⋮ Algebraic structures of degenerate systems and the indefinite metric ⋮ Von Neumann algebras and projections in space with conjugation operator ⋮ Invariant subspaces of operator algebras ⋮ Remarks on mathematical structure of BRST theories

Cites Work

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• Remarks on the reconstruction theorem for field theories with indefinite metric
• Tomita's theory of modular Hilbert algebras and its applications
• Quantisation in indefinite metric
• On the duality condition for a Hermitian scalar field
• JACQUES HADAMARD AND THE CREATION OF FUNCTIONAL ANALYSIS

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