Casimir Energy For a Massive Dirac Field in One Spatial Dimension: A Direct Approach

TL;DR

This paper calculates the Casimir energy for a massive Dirac field in one dimension using a direct mode summation method based on Boyer's approach, avoiding analytic continuation, and explores its dependence on distance and mass.

Contribution

It provides a direct, analytic calculation of Casimir energy for a massive fermionic field with MIT Bag boundary conditions without using analytic continuation.

Findings

Casimir energy as a function of distance and mass is explicitly plotted.

The method avoids analytic continuation techniques.

A rigorous derivation of the MIT Bag Model boundary condition is presented.

Abstract

In this paper we calculate the Casimir energy for a massive fermionic field confined between two points in one spatial dimension, with the MIT Bag Model boundary condition. We compute the Casimir energy directly by summing over the allowed modes. The method that we use is based on the Boyer's method, and there will be no need to resort to any analytic continuation techniques. We explicitly show the graph of the Casimir energy as a function of the distance between the points and the mass of the fermionic field. We also present a rigorous derivation of the MIT Bag Model boundary condition.