Euclidean spinor Green's functions in the spacetime of a straight cosmic string

TL;DR

This paper derives explicit forms of spinor Green's functions in conical Euclidean spaces and applies them to compute vacuum energy densities around cosmic strings, advancing understanding of quantum fields in such geometries.

Contribution

It provides a general method to compute spinor Green's functions in conical spaces and applies this to evaluate vacuum energies near cosmic strings.

Findings

Explicit spinor Green's functions in conical Euclidean space.

Vacuum energy density calculations for massless and massive spinor fields.

Results applicable to quantum field theory in cosmic string spacetimes.

Abstract

We determine generally the spinor Green's function and the twisted spinor Green's function in an Euclidean space with a conical-type line singularity. In particular, in the neighbourhood of the point source, we expree them as a sum of the usual Euclidean spinor Green's functin and a regular term. In four dimensions, we use these determinations to calculate the vacuum energy density and the twisted one for a massless spinor field in the spacetime of a straight cosmic string. In the Minkowski spacetime, we determine explicitly the vacuum energy density for a massive twisted spinor field.