Casimir Effect for Gauge Scalars: The Kalb-Ramond Case

TL;DR

This paper computes the Casimir energy for the Kalb-Ramond gauge field in 3+1 dimensions under boundary conditions analogous to conducting planes, comparing results with scalar and Maxwell fields.

Contribution

It provides the first calculation of the Casimir effect for the Kalb-Ramond field with specific boundary conditions, extending the understanding of gauge fields in confined geometries.

Findings

Casimir energy for the Kalb-Ramond field is derived.

Comparison with scalar and Maxwell fields highlights differences.

Boundary conditions influence the Casimir force for the gauge field.

Abstract

In this work we calculate the functional generator of the Green's functions of the Kalb-Ramond field in 3+1 dimensions. We also calculate the functional generator, and corresponding Casimir energy, of the same field when it is submitted to boundary conditions on two parallel planes. The boundary conditions we consider can be interpreted as a kind of conducting planes for the field in compearing with the Maxwell case. We compare our result with the standard ones for the scalar and Maxwell fields.