Motion of Spin 1/2 Massless Particle in a Curved Spacetime. II. Field Lagrangian Approach

TL;DR

This paper develops a field-theoretic approach to derive the equations of motion and spin dynamics of a massless spin 1/2 particle in curved spacetime, connecting classical and quantum descriptions.

Contribution

It introduces a field theory framework using Noether's theorem and Cartan's formalism to derive particle equations of motion and spin evolution in curved spacetime.

Findings

Equations reduce to particle worldline and spin equations under eikonal approximation.

Demonstrates consistency between classical quasi-classical and field-theoretic descriptions.

Provides a unified approach linking spinor field theory and particle dynamics in curved spacetime.

Abstract

Earlier we obtained quasi-classical equations of motion of spin 1/2 massless particle in a curved spacetime on base of simple Lagrangian model \cite{al2}. Now we suggest an approach to derive the equations in framework of field theory. Noether theorem formulated in terms of Cartan' formalism of orthonormal frames gives equations for current of spin of the field and tensor of stress-energy. It is shown that under eikonal approximation the above mentioned equations can be reduced to equations for worldline of the particle and equation of spin of the particle along the worldline. This way conformity between corpuscular considerations of spin 1/2 massless particle and approach in framework of spinor field theory in curved spacetime is demonstrated.