Krein structures for Wightman and Schwinger functions

DOI10.1063/1.527965zbMath0648.46065OpenAlexW2064275209MaRDI QIDQ3793215

Franco Strocchi, Lech Jakóbczyk

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1063/1.527965

zbMATH Keywords

analytic continuationSchwinger functionsKrein typecovariant formulation of free electrodynamicsEuclidean formulation of local field theory without positivityexistence of a Hilbert space structure for the space of vector statesKrein positivityKrein structureWightmann functions

Mathematics Subject Classification ID

Electromagnetic interaction; quantum electrodynamics (81V10) Constructive quantum field theory (81T08) Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Miscellaneous applications of functional analysis (46N99) Linear operators on spaces with an indefinite metric (47B50)

Related Items (8)

On algebra \(\sharp\)-cones in topological tensor-algebras. I: Basic properties and normality ⋮ An explicit realization of a GNS representation in a Krein-space ⋮ On the cones of \(\alpha\) and generalized \(\alpha\)-positivity for quantum field theories with indefinite metric ⋮ Unitarizable scalar multipoles ⋮ Unbounded GNS representations of a *-algebra in a Krein space ⋮ \(\alpha\)-positive/\(\alpha\)-negative definite functions on groups ⋮ Description of noncommutative theories and matrix models by Wightman functions ⋮ Euclidean field theory without reflection positivity. The case of photon field

Cites Work

• Spontaneous symmetry breaking in local gauge quantum field theory; the Higgs mechanism
• Axioms for Euclidean Green's functions. II

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