Generalised zeta-function regularization for scalar one-loop effective action

TL;DR

This paper extends zeta-function regularization to handle scalar fields in ultrastatic space-times with non-standard heat-kernel asymptotics, revealing new divergences and deriving renormalization group equations.

Contribution

It introduces a generalized zeta-function regularization method for scalar fields with unusual heat-kernel expansions, analyzing divergences and renormalization at one-loop level.

Findings

Additional divergences can occur at one-loop level.

The model's one-loop renormalizability is established.

Renormalization group equations are derived for the model.

Abstract

The one-loop effective action for a scalar field defined in the ultrastatic space-time where non standard logarithmic terms in the asymptotic heat-kernel expansion are present, 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 the one-loop renormalisation group equations are derived.