Curvature-spin coupling from the semi-classical limit of the Dirac equation

TL;DR

This paper derives a semi-classical model of a spinning particle in curved space-time from the Dirac equation, revealing a Papapetrou-like coupling between spin and curvature.

Contribution

It introduces a novel semi-classical spin-tensor from Dirac fields and demonstrates its coupling with space-time curvature, bridging quantum and classical descriptions.

Findings

Derived a semi-classical spin-tensor from Dirac fields.

Established a Papapetrou-like spin-curvature coupling.

Provided a framework connecting quantum spin to classical particle motion.

Abstract

The notion of a classical particle is inferred from Dirac quantum fields on a curved space-time, by an eikonal approximation and a localization hypothesis for amplitudes. This procedure allows to define a semi-classical version of the spin-tensor from internal quantum degrees of freedom, which has a Papapetrou-like coupling with the curvature.