Casimir energies for massive fields in the bag

TL;DR

This paper calculates the exact, renormalized Casimir energy for a massive scalar field confined in a spherical bag with Dirichlet boundary conditions, considering both interior and exterior regions, and highlights the differences from the massless case.

Contribution

It provides the first exact determination of the finite, renormalized zero-point energy for a massive field in a spherical geometry, including detailed renormalization procedures.

Findings

Exact finite parts of the Casimir energy for massive fields are obtained.

Renormalization constants are identified and can be experimentally determined.

Differences from the massless case are explicitly characterized.

Abstract

The Casimir energy corresponding to a massive scalar field with Dirichlet boundary conditions on a spherical bag is obtained. The field is considered, separately, inside and outside the bag. The renormalization procedure that is necessary to apply in each situation is studied in detail, in particular the differences occurring with respect to the case when the field occupies the whole space. The final result contains several constants that experience renormalization and can be determined only experimentally. The non-trivial finite parts that appear in the massive case are found exactly, providing a precise determination of the complete, renormalized zero-point energy for the first time.