Huygens' principle for the spin-1/2 particle in spacetime of non-constant curvature

TL;DR

This paper establishes conditions under which Huygens' principle applies to the Dirac equation for spin-1/2 particles in non-constant curvature cosmological spacetimes, considering both massless and massive cases.

Contribution

It provides necessary and sufficient conditions for Huygens' principle validity in non-constant curvature Friedmann-Lemaître-Robertson-Walker spacetimes for both massless and massive spin-1/2 particles.

Findings

Huygens' principle holds under specific geometric conditions.

Conditions are derived for both massless and massive particles.

Results relate to wave propagation in expanding universe models.

Abstract

In this article we give sufficient and necessary conditions for the validity of the Huygens' principle for the Dirac operator in the non-constant curvature spacetime of the Friedmann-Lema\^itre-Robertson-Walker models of cosmology. The Huygens' principle discussed for the equation of a particle with mass $m=0$ as well as a massive spin-1/2 particle (field) undergoing a red shift of its wavelength as the universe expands.