A Natural Renormalization of the One-Loop Effective Action for Scalar Field in Curved Space-time

TL;DR

This paper introduces a natural renormalization method for the one-loop effective action of scalar fields in curved space-time, utilizing negative norm states to automatically handle divergences.

Contribution

It extends the negative norm state approach to curved space-time, providing a natural renormalization procedure for the one-loop effective action.

Findings

Effective action calculated in general curved space-time

Automatic elimination of divergences achieved

Method applicable to quantum fields in curved backgrounds

Abstract

It has been shown that the negative norm states necessarily appear in a covariant quantization of the free minimally coupled scalar field in de Sitter space [1,2]. In this process ultraviolet and infrared divergences have been automatically eliminated [3]. A natural renormalization of the one-loop interacting quantum field in Minkowski space-time ($\lambda\phi^4$ theory) has been achieved through the consideration of the negative norm states [4]. One-loop effective action for scalar field in a general curved space-time has been calculated by this method and a natural renormalization procedure in the one-loop approximation has been established.