Spectral methods in quantum field theory and quantum cosmology

Details Spectral methods in quantum field theory and quantum cosmology Spectral methods in quantum field theory and quantum cosmology

2012-02-06

arxiv.org/abs/1202.1227v1

Physics

High Energy Physics

High Energy Physics - Theory

40 pages, Latex, submitted to the Stuart Dowker special issue of J. Phys. A

Scientific paper

We review the application of the spectral zeta-function to the 1- loop properties of quantum field theories on manifolds with boundary, with emphasis on Euclidean quantum gravity and quantum cosmology. As was shown in the literature some time ago, the only boundary conditions that are completely invariant under infinitesimal diffeomorphisms on metric perturbations suffer from a drawback, i.e. lack of strong ellipticity of the resulting boundary-value problem. Nevertheless, at least on the Euclidean 4-ball background, it remains possible to evaluate the zeta(0) value, which describes in this case a universe which, in the limit of small 3-geometry, has vanishing probability of approaching the cosmological singularity. An assessment of this result is here performed, discussing its physical and mathematical implications.

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