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Colosi, Daniele; Oeckl, Robert

Locality and general vacua in quantum field theory. (English) Zbl 1499.81014

SIGMA, Symmetry Integrability Geom. Methods Appl. 17, Paper 073, 83 p. (2021).
Summary: We extend the framework of general boundary quantum field theory (GBQFT) to achieve a fully local description of realistic quantum field theories. This requires the quantization of non-Kähler polarizations which occur generically on timelike hypersurfaces in Lorentzian spacetimes as has been shown recently. We achieve this in two ways: On the one hand we replace Hilbert space states by observables localized on hypersurfaces, in the spirit of algebraic quantum field theory. On the other hand we apply the GNS construction to twisted star-structures to obtain Hilbert spaces, motivated by the notion of reflection positivity of the Euclidean approach to quantum field theory. As one consequence, the well-known representation of a vacuum state in terms of a sea of particle pairs in the Hilbert space of another vacuum admits a vast generalization to non-Kähler vacua, particularly relevant on timelike hypersurfaces.

Cited in 1 Document

MSC:

81P16 Quantum state spaces, operational and probabilistic concepts
81S10 Geometry and quantization, symplectic methods
81S40 Path integrals in quantum mechanics
81T20 Quantum field theory on curved space or space-time backgrounds
81T70 Quantization in field theory; cohomological methods

Keywords:

quantum field theory; general boundary formulation; quantization; LSZ reduction formula; symplectic geometry; Feynman path integral; reflection positivity
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References:

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