Dirac particle in gravitational field

TL;DR

This paper derives new equations describing the motion of Dirac particles in gravitational fields, showing that their spin does not couple to curvature and linking wave packet spin to orbital angular momentum.

Contribution

It introduces modified world line equations for Dirac particles that differ from previous models and clarifies the relationship between spin and angular momentum in the zero-size limit.

Findings

Spin of Dirac particles does not couple to background curvature.

Wave packet spin is related to orbital angular momentum.

In the zero-size limit, total angular momentum contributions vanish.

Abstract

Classical dynamics of spinning zero-size objects in an external gravitational field is derived from the conservation law of the stress-energy and spin tensors. The resulting world line equations differ from those in the existing literature. In particular, the spin of the Dirac particle does not couple to the background curvature. As a check of consistency, the wave packet solution of the free Dirac equation is considered. The resulting equations are shown to include a constraint that relates the wave packet spin to its orbital angular momentum. In the zero-size limit, both contributions to the total angular momentum disappear simultaneously.