Calculation of the Regularized Vacuum Energy in Cavity Field Theories

TL;DR

This paper introduces a new method using Schwinger's proper time approach to calculate regularized vacuum energies in cavity field theories, specifically for the MIT bag model, with improved numerical control and insights into divergence cancellations.

Contribution

It applies a novel technique to compute vacuum energies in cavity models, providing more accurate results and exploring divergence cancellations in the MIT bag model.

Findings

Results partly agree with previous asymptotic methods.

Numerical errors are better controlled with the new technique.

Boundary divergence cancellations do not occur in the fermionic case.

Abstract

A novel technique based on Schwinger's proper time method is applied to the Casimir problem of the M.I.T. bag model. Calculations of the regularized vacuum energies of massless scalar and Dirac spinor fields confined to a static and spherical cavity are presented in a consistent manner. While our results agree partly with previous calculations based on asymptotic methods, the main advantage of our technique is that the numerical errors are under control. Interpreting the bag constant as a vacuum expectation value, we investigate potential cancellations of boundary divergences between the canonical energy and its bag constant counterpart in the fermionic case. It is found that such cancellations do not occur.