Effective action for scalar fields and generalised zeta-function regularisation

Abstract

Motivated by the study of quantum fields in a Friedman-Robertson-Walker (FRW) spacetime, the one-loop effective action for a scalar field defined in the ultrastatic manifold $R\times H^3/\Gamma$, $H^3/\Gamma$ being the finite volume, non-compact, hyperbolic spatial section, is investigated by a generalisation of zeta-function regularisation. It is shown that additional divergences may appear at one-loop level. The one-loop renormalisability of the model is discussed and making use of a generalisation of zeta-function regularisation, the one-loop renormalisation group equations are derived.

Latex, 16 pages, no figures; Latex mistakes corrected; accepted for publication in Physical Review D

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• Zeta Determinant for Laplace Operators on Riemann Caps
• Quantum probing of null-singularities
• The spectral $\zeta$-function for quasi-regular Sturm--Liouville operators
• Generalized Zeta Function Regularization and the Multiplicative Anomaly
• Generalised zeta-function regularization for scalar one-loop effective action