Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-04-05
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
5 pages, Revtex, paper prepared for the QG5 parallel session on Quantum Cosmology at 9th Marcel Grossmann Meeting on Recent De
Scientific paper
In a path-integral approach to quantum cosmology, the Lorenz gauge-averaging term is studied for Euclidean Maxwell theory on a portion of flat four-space bounded by two concentric three-spheres, but with arbitrary values of the gauge parameter. The resulting set of eigenvalue equations for normal and longitudinal modes of the electromagnetic potential cannot be decoupled, and is here studied with a Green-function method. This means that an equivalent equation for longitudinal modes is obtained which has integro-differential nature, after inverting a differential operator in the original coupled system. A complete calculational scheme is therefore obtained for the one-loop semiclassical evaluation of the wave function of the universe in the presence of gauge fields. This might also lead to a better understanding of how gauge independence is actually achieved on manifolds with boundary, whose consideration cannot be avoided in a quantum theory of the universe.
Esposito Giampiero
Pollifrone Giuseppe
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