Topology, Mass and Casimir energy

TL;DR

This paper calculates the Casimir energy for massive scalar, spinor, and twisted fields in spaces with non-trivial topology using an optical path approach, revealing mass and temperature effects on vacuum energy.

Contribution

It introduces an optical method based on classical paths to evaluate Casimir energy for various fields in complex topologies, including mass and temperature dependencies.

Findings

Massive fields significantly affect Casimir energy at high and low temperatures.

The optical approach effectively computes contributions from different topologies and field types.

Results align with and extend previous literature on vacuum energies in non-trivial spaces.

Abstract

The vacuum expectation value of the stress energy tensor for a massive scalar field with arbitrary coupling in flat spaces with non-trivial topology is discussed. We calculate the Casimir energy in these spaces employing the recently proposed {\it optical approach} based on closed classical paths. The evaluation of the Casimir energy consists in an expansion in terms of the lengths of these paths. We will show how different paths with corresponding weight factors contribute in the calculation. The optical approach is also used to find the mass and temperature dependence of the Casimir energy in a cavity and it is shown that the massive fields cannot be neglected in high and low temperature regimes. The same approach is applied to twisted as well as spinor fields and the results are compared with those in the literature.