Spinor Green function in higher-dimensional cosmic string space-time in the presence of magnetic flux

TL;DR

This paper derives the Green function for quantum fermionic fields in higher-dimensional cosmic string space-times with magnetic flux, analyzing vacuum polarization effects and calculating renormalized energy-momentum tensors.

Contribution

It provides a general Green function expression for various dimensions and explicit results for massless and massive fields in cosmic string backgrounds with magnetic flux.

Findings

Derived a general Green function for different dimensions.

Calculated renormalized vacuum expectation values of energy-momentum tensors.

Presented closed-form solutions for specific parameters and massive fields.

Abstract

In this paper we investigate the vacuum polarization effects associated with quantum fermionic charged fields in a generalized $(d+1)-$dimensional cosmic string space-times considering the presence of a magnetic flux along the string. In order to develop this analysis we calculate a general expression for the respective Green function, valid for several different values of $d$, which is expressed in terms of a bispinor associated with the square of the Dirac operator. Adopting this result, we explicitly calculate the renormalized vacuum expectation values of the energy-momentum tensors, $<T^A_B>_{Ren.}$, associated with massless fields. Moreover, for specific values of the parameters which codify the cosmic string and the fractional part of the ratio of the magnetic flux by the quantum one, we were able to present in closed forms the bispinor and the respective Green function for massive fields.