Effective action for scalar fields and generalized zeta-function regularization

Abstract

Motivated by the study of quantum fields in a Friedmann-Robertson-Walker space-time, the one-loop effective action for a scalar field defined in the ultrastatic manifold $R\ifmmode\times\else\texttimes\fi{}{H}^{3}/\ensuremath{\Gamma},$ ${H}^{3}/\ensuremath{\Gamma}$ being the finite volume, noncompact, hyperbolic spatial section, is investigated by a generalization of zeta-function regularization. It is shown that additional divergences may appear at the one-loop level. The one-loop renormalizability of the model is discussed and, making use of a generalization of zeta-function regularization, the one-loop renormalization group equations are derived.