Gupta-Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times

Finster, Felix and Strohmaier, Alexander (2015) Gupta-Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times. ANNALES HENRI POINCARE, 16 (8). pp. 1837-1868. ISSN 1424-0637, 1424-0661

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Abstract

We give a complete framework for the Gupta-Bleuler quantization of the free electromagnetic field on globally hyperbolic space-times. We describe one-particle structures that give rise to states satisfying the microlocal spectrum condition. The field algebras in the so-called Gupta-Bleuler representations satisfy the time-slice axiom, and the corresponding vacuum states satisfy the microlocal spectrum condition. We also give an explicit construction of ground states on ultrastatic space-times. Unlike previous constructions, our method does not require a spectral gap or the absence of zero modes. The only requirement, the absence of zero-resonance states, is shown to be stable under compact perturbations of topology and metric. Usual deformation arguments based on the time-slice axiom then lead to a construction of Gupta-Bleuler representations on a large class of globally hyperbolic space-times. As usual, the field algebra is represented on an indefinite inner product space, in which the physical states form a positive semi-definite subspace. Gauge transformations are incorporated in such a way that the field can be coupled perturbatively to a Dirac field. Our approach does not require any topological restrictions on the underlying space-time.

Item Type: Article
Uncontrolled Keywords: QUANTUM-FIELDS; ORDERED PRODUCTS; WICK POLYNOMIALS; SUPERSELECTION; OBSERVABLES; MANIFOLDS; CHARGE; SETS;
Subjects: 500 Science > 510 Mathematics
Divisions: Mathematics > Prof. Dr. Felix Finster
Depositing User: Dr. Gernot Deinzer
Date Deposited: 03 Jul 2019 11:45
Last Modified: 03 Jul 2019 11:45
URI: https://pred.uni-regensburg.de/id/eprint/5148

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