Functional approach to the fermionic Casimir effect

TL;DR

This paper develops a functional method to compute the fermionic Casimir effect with imperfect boundary conditions, providing explicit energy formulas in various dimensions and for different field masses.

Contribution

It introduces a novel functional approach to model bag-like boundary conditions via delta interactions, enabling explicit Casimir energy calculations.

Findings

Explicit formulas for Casimir energies in 1+1 and 3+1 dimensions.

Proper implementation of bag boundary conditions through coupling constants.

Applicability to both massless and massive fermionic fields.

Abstract

We use a functional approach to calculate the Casimir energy due to Dirac fields in interaction with thin, flat, parallel walls, which implement imperfect bag-like boundary conditions. These are simulated by the introduction of delta-like interactions with the walls. We show that, with a proper choice for the corresponding coupling constants, bag-model boundary condition are properly implemented. We obtain explicit expressions for the energies in 1+1 and 3+1 dimensions, for massless and massive fields.