Conservation of the Dirac Current in Models with a General Spin Connection

TL;DR

This paper derives conditions for conserving the Dirac current in models with a general spin connection, extending previous assumptions and applying these to a specific model from prior literature.

Contribution

It establishes the necessary conditions for Dirac current conservation when generalizing the spin connection beyond the standard assumption.

Findings

Derived explicit conditions for Dirac current conservation.

Applied conditions to a specific model from prior research.

Provided a framework for analyzing spin connection effects on Dirac fields.

Abstract

Here I obtain the conditions necessary for the conservation of the Dirac current when one substitutes the assumption $\gamma^A_{\ \ |B}=0$ for $\gamma^A_{\ \ |B}=[V_B,\gamma^A]$, where the $\gamma^A$s are the Dirac matrices and "$|$" represents the components of the covariant derivative. As an application, I apply these conditions to the model used in Ref. [M. Novello, Phys. Rev. {\bf D8}, 2398 (1973)].