Casimir energy calculation for massive scalar field on spherical surfaces: an alternative approach

TL;DR

This paper introduces a direct, physically meaningful method for calculating Casimir energy of a massive scalar field on spherical surfaces, simplifying the renormalization process and aligning well with previous results.

Contribution

The study proposes a novel direct approach for Casimir energy calculation that reduces manual renormalization and enhances physical interpretation.

Findings

The new method aligns with previous results in various topologies.

Automatic renormalization occurs in the large mass limit for S^2.

The approach provides clearer physical insight into Casimir energy calculations.

Abstract

In this study, the Casimir energy for massive scalar field with periodic boundary condition was calculated on spherical surfaces with $S^1$, $S^2$ and $S^3$ topologies. To obtain the Casimir energy on spherical surface, the contribution of the vacuum energy of Minkowski space is usually subtracted from that of the original system. In large mass limit for surface $S^2$; however, some divergences would eventually remain in the obtained result. To remove these remaining divergences, a secondary renormalization program was manually performed. In the present work, a direct approach for calculation of the Casimir energy has been introduced. In this approach, two similar configurations were considered and then the vacuum energies of these configurations were subtracted from each other. This method provides more physical meaning respect to the other common methods. Additionally, in large mass limit for surface $S^2$, it provides a situation in which the second renormalization program is automatically conducted in the calculation procedure, and there was no need to do that anymore manually. Finally, by plotting the obtained values for the Casimir energy of the topologies and investigating their appropriate limits, the logic agreement between the results of our scheme and those of previous studies were discussed.