Fermionic vacuum polarization by a flat boundary in cosmic string spacetime

TL;DR

This paper studies how a flat boundary affects the vacuum polarization of a massive fermionic field in cosmic string spacetime, providing explicit formulas and analyzing the behavior of vacuum expectation values.

Contribution

It offers new explicit formulas for fermionic vacuum expectation values in cosmic string spacetime with a boundary, considering MIT bag boundary conditions.

Findings

Boundary-induced effects vanish for massless fields.

Total energy density is negative everywhere.

Radial stress equals energy density for massive fields.

Abstract

In this paper we investigate the fermionic condensate and the renormalized vacuum expectation value (VEV) of the energy-momentum tensor for a massive fermionic field induced by a flat boundary in the cosmic string spacetime. In this analysis we assume that the field operator obeys MIT bag boundary condition on the boundary. We explicitly decompose the VEVs into the boundary-free and boundary-induced parts. General formulas are provided for both parts which are valid for any value of the parameter associated with the cosmic string. For a massless field, the boundary-free part in the fermionic condensate and the boundary-induced part in the energy-momentum tensor vanish. For a massive field the radial stress is equal to the energy density for both boundary-free and boundary-induced parts. The boundary-induced part in the stress along the axis of the cosmic string vanishes. The total energy density is negative everywhere, whereas the effective pressure along the azimuthal direction is positive near the boundary and negative near the cosmic string. We show that for points away from the boundary, the boundary-induced parts in the fermionic condensate and in the VEV of the energy-momentum tensor vanish on the string.