Tomaschitz, R. (2001). Electromagnetic propagators in hyperbolic Robertson-Walker cosmologies, Journal of Mathematical Physics 42, 5800-5831, 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 3-manifolds 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 3-sections. The time and space components of the resolvent kernel are scalar and vectorial point-pair 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 3-spaces. In cosmologies with multiply connected hyperbolic 3-manifolds 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 3-spaces, including those with Schottky covering groups corresponding to solid handle-bodies 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 Robertson-Walker cosmologies.
[J] J.
Math. Phys. 42, No.12, 5800-5831 (2001). ISSN 0022-2488
MSC 2000
*83C50
Electromagnetic fields
83F05 Relativistic cosmology
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Title: |
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Electromagnetic propagators in hyperbolic Robertson-Walker cosmologies |
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Authors: |
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Tomaschitz, Roman |
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AA(Department of Physics, Hiroshima University, 1-3-1 Kagami-yama, Higashi-Hiroshima 739-8526, Japan) |
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Journal of Mathematical Physics, Volume 42, Issue 12, pp. 5800-5831 (2001). |
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12/2001 |
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PACS Keywords: |
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Classical electromagnetism, Maxwell equations, Function theory, analysis |
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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 3-space, constant negative curvature, scalar and vectorial point-pair invariants, Poincaré half-space, Poincaré series, Eisenstein series, open hyperbolic 3-manifolds, Schottky groups, Kleinian groups, spectral geometry, hyperbolic geometry
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