Fermionic vacuum polarization by a flat boundary in cosmic string spacetime

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.