Tomaschitz, R. (2001). Electromagnetic propagators in hyperbolic RobertsonWalker cosmologies, Journal of Mathematical Physics 42, 58005831, DOI: 10.1063/1.1413522
Abstract (AIP, SAO/NASA ADS, Zbl 1009.83025)
Green functions (retarded, advanced, Feynman and Dyson propagators) are calculated for the electromagnetic field in Robertson–Walker cosmologies with hyperbolic 3manifolds as spacelike slices. The starting point is the Proca equation, i.e., the Maxwell field with a finite photon mass for infrared regularization, in a static cosmology with simply connected hyperbolic 3sections. The time and space components of the resolvent kernel are scalar and vectorial pointpair invariants, respectively, and this symmetry allows for an explicit evaluation in the spectral representation. It is found that the quantum propagators have a logarithmic infrared singularity, which drops out in the zero curvature limit. Retarded and advanced Green functions remain well defined in the limit of zero photon mass, and they admit a simple generalization, by conformal scaling, to expanding 3spaces. In cosmologies with multiply connected hyperbolic 3manifolds as spacelike sections, the four enumerated propagators are constructed by means of Poincaré series. The spectral decomposition of the Green functions is given in terms of Eisenstein series for a certain class of open hyperbolic 3spaces, including those with Schottky covering groups corresponding to solid handlebodies as spacelike slices.
Keywords
cosmology, electromagnetic field theory, Green's function methods, Maxwell equations
98.80.Jk
Mathematical and relativistic aspects of cosmology
03.50.De
Classical electromagnetism, Maxwell equations
02.30.f
Function theory, analysis
Zbl
1009.83025
Tomaschitz, Roman
Electromagnetic propagators in hyperbolic RobertsonWalker cosmologies.
[J] J.
Math. Phys. 42, No.12, 58005831 (2001). ISSN 00222488
MSC 2000
*83C50
Electromagnetic fields
83F05 Relativistic cosmology
Title: 

Electromagnetic propagators in hyperbolic RobertsonWalker cosmologies 
Authors: 

Tomaschitz, Roman 
Affiliation: 

AA(Department of Physics, Hiroshima University, 131 Kagamiyama, HigashiHiroshima 7398526, Japan) 
Publication: 

Journal of Mathematical Physics, Volume 42, Issue 12, pp. 58005831 (2001). 
Publication Date: 

12/2001 
Origin: 


PACS Keywords: 

Classical electromagnetism, Maxwell equations, Function theory, analysis 
DOI: 


Bibliographic Code: 

description: Roman Tomaschitz (2001) Electromagnetic propagators in hyperbolic Robertson–Walker cosmologies, Journal of Mathematical Physics 42, 5800.
Keywords: Robertson–Walker cosmology, electrodynamics, retarded and advanced electromagnetic Green functions, Feynman and Dyson propagators, infrared regularization, photon mass, Proca equation, Maxwell equations, multiply connected hyperbolic 3space, constant negative curvature, scalar and vectorial pointpair invariants, Poincaré halfspace, Poincaré series, Eisenstein series, open hyperbolic 3manifolds, Schottky groups, Kleinian groups, spectral geometry, hyperbolic geometry
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