Motion of a Vector Particle in a Curved Spacetime. I. Lagrangian Approach

TL;DR

This paper derives equations of motion for spinning and massless particles in curved spacetime using a Lagrangian approach, showing spin conservation and reduction to geodesics when spin is absent.

Contribution

It introduces a Lagrangian framework for describing vector particle motion in curved spacetime, including spin effects and massless cases.

Findings

Spin is conserved along the particle's world-line.

Equations reduce to geodesic motion when spin is zero.

Applicable to both massive and massless particles.

Abstract

From the simple Lagrangian the equations of motion for the particle with spin are derived. The spin is shown to be conserved on the particle world-line. In the absence of a spin the equation coincides with that of a geodesic. The equations of motion are valid for massless particles as well, since mass does not enter the equations explicitely.