On a possible method of Casimir pressure renormalization in a ball

TL;DR

This paper introduces a novel renormalization method for Casimir pressure in a spherical geometry, resulting in an exponential mass dependence and avoiding exterior domain complications.

Contribution

It presents an alternative renormalization approach that differs from standard methods, simplifying calculations and changing the mass dependence of Casimir pressure.

Findings

Pressure depends exponentially on the mass of the scalar field.

The method avoids using the exterior domain scalar field.

It offers a simplified and alternative renormalization procedure.

Abstract

We propose a method of Casimir pressure renormalization for massive scalar field in a ball. This method is slightly different from the generally accepted. An alternative way of choosing the normalization point leads to an exponential pressure dependence on the mass of the field instead of an inverse polynomial dependence. The method proposed does not use the scalar quantized field in the exterior domain. This allows us to bypass the difficulties that appear when one uses the standard approach.