Finster, F and Strohmaier, A orcid.org/0000-0002-8446-3840 (2015) Gupta–Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times. Annales Henri Poincaré, 16 (8). pp. 1837-1868. ISSN 1424-0637
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Springer Basel. This is an author produced version of a paper published in Annales Henri Poincaré. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at Springer via Annales Henri Poincaré. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 05 Apr 2017 15:04 |
Last Modified: | 16 Jan 2018 15:47 |
Published Version: | https://doi.org/10.1007/s00023-014-0363-z |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s00023-014-0363-z |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111673 |
Commentary/Response Threads
- Finster, F and Strohmaier, A Gupta–Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times. (deposited 05 Apr 2017 15:04) [Currently Displayed]