Dirac equation in spacetimes with torsion and non-metricity

TL;DR

This paper extends the Dirac equation to non-Riemannian spacetimes with torsion and non-metricity, analyzing their effects on spinning particles in a Schwarzschild background, revealing small but fundamental couplings.

Contribution

It formulates the Dirac equation in spacetimes with torsion and non-metricity and explores their coupling to particle momentum and spin.

Findings

Torsion and non-metricity couple to momentum and spin.

Effects are too small for current observational detection.

Analysis performed in Schwarzschild background.

Abstract

Dirac equation is written in a non-Riemannian spacetime with torsion and non-metricity by lifting the connection from the tangent bundle to the spinor bundle over spacetime. Foldy-Wouthuysen transformation of the Dirac equation in a Schwarzschild background spacetime is considered and it is shown that both the torsion and non-metricity couples to the momentum and spin of a massive, spinning particle. However, the effects are small to be observationally significant.