Spin-weighted Green's functions in a conical space

TL;DR

This paper analyzes spin-weighted Green's functions in conical spaces, deriving explicit forms for massless spin 1/2 and electromagnetic fields around cosmic strings and in Rindler space, including zero-temperature cases.

Contribution

It provides a detailed derivation of Euclidean Green's functions for spinor and electromagnetic fields in conical geometries, extending previous scalar field results.

Findings

Green's functions for massless spin 1/2 and electromagnetic fields are obtained.

Zero-temperature Green's functions are explicitly derived.

These functions generally do not match thermal Feynman Green's functions for non-scalar fields.

Abstract

We give an analysis of the spin-weighted Green's functions well-defined in a conical space. We apply these results in the case of a straight cosmic string and in the Rindler space in order to determine generally the Euclidean Green's functions for the massless spin 1/2 field and for the electromagnetic field. We give also the corresponding Green's functions at zero temperature. However, except for the scalar field, it seems that these Euclidean Green's functions do not correspond to the thermal Feynman Green's functions.