Irreducibility and reducing subspaces for Krein space representations of field algebra

DOI10.1063/1.529977zbMath0769.46046OpenAlexW1989184984MaRDI QIDQ4032281

Lech Jakóbczyk

Publication date: 1 April 1993

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

Full work available at URL: https://doi.org/10.1063/1.529977

zbMATH Keywords

quantum field theoriesreducing subspacesWightman stateexistence of nontrivial Krein selfadjoint subspacesfundamental symmetry of the Krein spaceKrein-adjoint representationKrein-Hermitian representationKrein-Hermitian representationsrepresentations of the Borchers \(^*\)-algebrastrong commutantthree types of commutantsweak Hilbert commutantweak Krein commutant

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Axiomatic quantum field theory; operator algebras (81T05) Applications of selfadjoint operator algebras to physics (46L60)

Cites Work

• On field algebras in quantum theory with indefinite metric
• Unbounded GNS representations of a *-algebra in a Krein space
• Self-adjoint algebras of unbounded operators
• Some algebras of unbounded operators in an indefinite inner product vector space

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