Casimir energy of massive MIT fermions in a Bohm-Aharonov background

TL;DR

This paper investigates how a background flux string influences the vacuum energy of massive Dirac fermions in 2+1 dimensions within a finite region, revealing discontinuities at certain flux values.

Contribution

It compares two self-adjoint extensions of the Hamiltonian to analyze their effects on the Casimir energy in the presence of a flux string.

Findings

Casimir energy is affected by the background flux string.

Discontinuity in Casimir energy occurs at integer flux values for one extension.

Comparison of two Hamiltonian extensions highlights different physical behaviors.

Abstract

We study the effect of a background flux string on the vacuum energy of massive Dirac fermions in 2+1 dimensions confined to a finite spatial region through MIT boundary conditions. We treat two admissible self-adjoint extensions of the Hamiltonian and compare the results. In particular, for one of these extensions, the Casimir energy turns out to be discontinuous at integer values of the flux.