Tomaschitz, R. (2001). Electromagnetic propagators in hyperbolic Robertson-Walker cosmologies, Journal of Mathematical Physics 42, 5800-5831, DOI: 10.1063/1.1413522



Abstract (AIPSAO/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.



cosmology, electromagnetic field theory, Green's function methods, Maxwell equations




Mathematical and relativistic aspects of cosmology


Classical electromagnetism, Maxwell equations


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






Electromagnetic propagators in hyperbolic Robertson-Walker cosmologies



Tomaschitz, Roman



AA(Department of Physics, Hiroshima University, 1-3-1 Kagami-yama, Higashi-Hiroshima 739-8526, Japan)



Journal of Mathematical Physics, Volume 42, Issue 12, pp. 5800-5831 (2001).

Publication Date:






PACS Keywords:


Classical electromagnetism, Maxwell equations, Function theory, analysis




Bibliographic Code:




description: Roman Tomaschitz (2001) Electromagnetic propagators in hyperbolic RobertsonWalker cosmologies, Journal of Mathematical Physics 42, 5800.


Keywords: RobertsonWalker 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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