Mathisson-Papapetrou equations in metric and gauge theories of gravity in a Lagrangian formulation

TL;DR

This paper introduces a straightforward Lagrangian-based method to derive semiclassical equations of motion for spinning particles in various gravitational theories, including metric and gauge theories, aligning with established results.

Contribution

It provides a novel, simplified approach to derive spin and momentum evolution equations without explicit matter current densities in metric and gauge gravity theories.

Findings

Method reproduces known equations for spinning particles in gravity.

Applicable to classical and elementary particles with intrinsic spin.

Results align with traditional multipole and WKB analyses.

Abstract

We present a simple method to derive the semiclassical equations of motion for a spinning particle in a gravitational field. We investigate the cases of classical, rotating particles (pole-dipole particles), as well as particles with intrinsic spin. We show that, starting with a simple Lagrangian, one can derive equations for the spin evolution and momentum propagation in the framework of metric theories of gravity and in theories based on a Riemann-Cartan geometry (Poincare gauge theory), without explicitly referring to matter current densities (spin and energy-momentum). Our results agree with those derived from the multipole expansion of the current densities by the conventional Papapetrou method and from the WKB analysis for elementary particles.