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Finster, Felix ; Strohmaier, Alexander

Gupta-Bleuler quantization of the Maxwell field in globally hyperbolic space-time

Finster, Felix and Strohmaier, Alexander (2013) Gupta-Bleuler quantization of the Maxwell field in globally hyperbolic space-time. Preprintreihe der Fakultät Mathematik 13/2013, Working Paper.

Date of publication of this fulltext: 14 Oct 2013 08:17
Monograph
DOI to cite this document: 10.5283/epub.28911


Abstract

We give a complete framework for the Gupta-Bleuler quantization of the free electromagnetic field on globally hyperbolic space-times. We describe oneparticle structures that give rise to states satisfying the microlocal spectrum condition. The field algebra in the so-called Gupta-Bleuler representations satisfies the time-slice axiom, and the corresponding vacuum states satisfy the ...

We give a complete framework for the Gupta-Bleuler quantization of
the free electromagnetic field on globally hyperbolic space-times. We describe oneparticle
structures that give rise to states satisfying the microlocal spectrum condition.
The field algebra in the so-called Gupta-Bleuler representations satisfies
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.


Involved Institutions


Details

Item typeMonograph (Working Paper)
Series of the University of Regensburg:Preprintreihe der Fakultät Mathematik
Volume:13/2013
Date2013
InstitutionsMathematics > Prof. Dr. Felix Finster
Dewey Decimal Classification500 Science > 510 Mathematics
StatusUnknown
RefereedNo, this version has not been refereed yet (as with preprints)
Created at the University of RegensburgYes
URN of the UB Regensburgurn:nbn:de:bvb:355-epub-289114
Item ID28911

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