Zeta Functions and the Casimir Energy

TL;DR

This paper employs zeta function methods to define and analyze the Casimir energy in ultrastatic spacetimes, revealing its dependence on normalization scales and its implications for quantum field theories and cosmology.

Contribution

It introduces a zeta function approach to finite Casimir energy in arbitrary ultrastatic spacetimes, clarifying its relation to effective energy and scale dependence.

Findings

Casimir energy depends on a normalization scale.

The method applies to spacetimes with boundaries.

One-loop corrections to cosmological constants are calculable.

Abstract

We use zeta function techniques to give a finite definition for the Casimir energy of an arbitrary ultrastatic spacetime with or without boundaries. We find that the Casimir energy is intimately related to, but not identical to, the one-loop effective energy. We show that in general the Casimir energy depends on a normalization scale. This phenomenon has relevance to applications of the Casimir energy in bag models of QCD. Within the framework of Kaluza-Klein theories we discuss the one-loop corrections to the induced cosmological and Newton constants in terms of a Casimir like effect. We can calculate the dependence of these constants on the radius of the compact dimensions, without having to resort to detailed calculations.