Fermionic vacuum polarization by a cylindrical boundary in the cosmic string spacetime

TL;DR

This paper investigates how a cylindrical boundary affects fermionic vacuum polarization in cosmic string spacetime, providing explicit formulas and analyzing behavior in various limits, including Minkowski space as a special case.

Contribution

It introduces a method to separate boundary-induced effects from cosmic string geometry in fermionic vacuum expectation values, simplifying renormalization.

Findings

Boundary effects are exponentially suppressed for large angle deficits.

Explicit integral formulas for vacuum densities are derived.

Vacuum densities are analyzed in different asymptotic regimes.

Abstract

The vacuum expectation values of the energy--momentum tensor and the fermionic condensate are analyzed for a massive spinor field obeying the MIT bag boundary condition on a cylindrical shell in the cosmic string spacetime. Both regions inside and outside the shell are considered. By applying to the corresponding mode-sums a variant of the generalized Abel--Plana formula, we explicitly extract the parts in the expectation values corresponding to the cosmic string geometry without boundaries. In this way the renormalization procedure is reduced to that for the boundary-free cosmic string spacetime. The parts induced by the cylindrical shell are presented in terms of integrals rapidly convergent for points away from the boundary. The behavior of the vacuum densities is investigated in various asymptotic regions of the parameters. In the limit of large values of the planar angle deficit, the boundary-induced expectation values are exponentially suppressed. As a special case, we discuss the fermionic vacuum densities for the cylindrical shell on the background of the Minkowski spacetime.