Lagrangian for the Frenkel electron

TL;DR

This paper derives a Lagrangian for a spinning particle using a non-Grassmann vector, generalizing Frenkel and BMT equations to arbitrary electromagnetic fields, and discusses ultra-relativistic motion with anomalous magnetic moments.

Contribution

It introduces a new Lagrangian formulation for spinning particles with a single auxiliary variable, extending existing equations to more general electromagnetic scenarios.

Findings

Provides a consistent Lagrangian for spinning particles.

Generalizes Frenkel and BMT equations.

Analyzes ultra-relativistic behavior with anomalous magnetic moments.

Abstract

We found Lagrangian action which describes spinning particle on the base of non-Grassmann vector and involves only one auxiliary variable. It provides the right number of physical degrees of freedom and yields generalization of the Frenkel and BMT equations to the case of an arbitrary electromagnetic field. For a particle with anomalous magnetic moment, singularity in the relativistic equations generally occurs at the speed different from the speed of light. Detailed discussion of the ultra-relativistic motion is presented in the work: A. A. Deriglazov and W. G. Ramirez, World-line geometry probed by fast spinning particle, arXiv:1409.4756.