Variational problem for the Frenkel and the Bargmann-Michel-Telegdi (BMT) equations

TL;DR

This paper develops a Lagrangian formulation for classical spinning particles, incorporating gauge invariance and quantum corrections, to better understand the dynamics described by the Frenkel and BMT equations.

Contribution

It introduces a gauge-invariant Lagrangian framework for classical spin particles, connecting Frenkel tensor and BMT vector descriptions with quantum corrections.

Findings

Lagrangian invariant under non-abelian gauge group

Gauge-invariant variables include Frenkel tensor and BMT vector

Classical spin fixation leads to quantum corrections in equations of motion

Abstract

We propose Lagrangian formulation for the particle with value of spin fixed within the classical theory. The Lagrangian turns out to be invariant under non-abelian group of local symmetries. As the gauge-invariant variables for description of spin we can take either the Frenkel tensor or the BMT vector. Fixation of spin within the classical theory implies $O(\hbar)$-corrections to the corresponding equations of motion.