Spinor Parallel Propagator and Green's Function in Maximally Symmetric Spaces

TL;DR

This paper introduces a covariant spinor parallel propagator for maximally symmetric spaces and derives the Dirac spinor Green's functions in these spaces, providing a geometric and coordinate-independent framework.

Contribution

The paper presents the first explicit construction of a spinor parallel propagator and Green's functions in maximally symmetric spaces of any dimension, enhancing geometric understanding.

Findings

Explicit form of the spinor parallel propagator derived

Green's functions expressed in terms of intrinsic geometric objects

Results are covariant and coordinate-independent

Abstract

We introduce the spinor parallel propagator for maximally symmetric spaces in any dimension. Then, the Dirac spinor Green's functions in the maximally symmetric spaces R^n, S^n and H^n are calculated in terms of intrinsic geometric objects. The results are covariant and coordinate-independent.