Fundamental solutions of the Dirac operator in the Friedmann-Lema\^itre-Robertson-Walker spacetime

TL;DR

This paper derives explicit fundamental solutions for the Dirac operator in Friedmann-Lemaître-Robertson-Walker spacetime, linking them to Minkowski wave solutions, advancing understanding of spin-$rac{1}{2}$ particles in cosmological models.

Contribution

It provides explicit formulas for fundamental solutions of the Dirac operator in a cosmological spacetime, connecting them to Minkowski wave solutions, which is a novel analytical development.

Findings

Explicit fundamental solutions for the Dirac operator are obtained.

Solutions are expressed via Minkowski wave equation fundamental solutions.

The work enhances analytical tools for quantum fields in cosmological backgrounds.

Abstract

The equation of the spin-$\frac{1}{2}$ particles in the Friedmann-Lema\^itre-Robertson-Walker spacetime is investigated. The retarded and advanced fundamental solutions to the Dirac operator and generalized Dirac operator as well as the fundamental solutions to the Cauchy problem are written in explicit form via the fundamental solution of the wave equation in the Minkowski spacetime.