Fermionic Casimir densities in a conical space with a circular boundary and magnetic flux

TL;DR

This paper analyzes the vacuum expectation value of the energy-momentum tensor for a massive fermionic field in a conical space with a circular boundary and magnetic flux, revealing effects like the Aharonov-Bohm phenomenon and boundary-induced vacuum energy variations.

Contribution

It provides a detailed calculation of the fermionic vacuum energy in a conical geometry with boundaries and magnetic flux, including boundary effects and special boundary conditions.

Findings

Vacuum energy density is negative inside the circle for massless fields.

Boundary-induced effects dominate near the circular boundary.

Vacuum expectation values are periodic functions of magnetic flux with flux quantum period.

Abstract

The vacuum expectation value (VEV) of the energy-momentum tensor for a massive fermionic field is investigated in a (2+1)-dimensional conical spacetime in the presence of a circular boundary and an infinitely thin magnetic flux located at the cone apex. The MIT bag boundary condition is assumed on the circle. At the cone apex we consider a special case of boundary conditions for irregular modes, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The presence of the magnetic flux leads to the Aharonov-Bohm-like effect on the VEV of the energy-momentum tensor. For both exterior and interior regions, the VEV is decomposed into boundary-free and boundary-induced parts. Both these parts are even periodic functions of the magnetic flux with the period equal to the flux quantum. The boundary-free part in the radial stress is equal to the energy density. Near the circle, the boundary-induced part in the VEV dominates and for a massless field the vacuum energy density is negative inside the circle and positive in the exterior region. Various special cases are considered.