Derivation of the Classical Lagrangian for the Relativistic Spinning Particle

TL;DR

This paper derives a classical model for a relativistic spinning particle from the isotropic rotator, clarifying the role of additional variables and constraints in the covariant formulation.

Contribution

It provides a derivation of the classical spinning particle model from the isotropic rotator, elucidating the significance of extra variables and constraints.

Findings

Spin as a relativistic extension of the isotropic rotator

Necessary variables for covariant formulation identified

Clarification of the constraint term and its relation to quasi-supersymmetry

Abstract

The `classical' model for a massive spinning particle, which was recently proposed, is derived from the isotropic rotator model. Through this derivation, we note that the spin can be understood as the relativistic extension of the isotropic rotator. Furthermore, the variables $t_\m$ corresponding to the $\p^*$ of the `pseudo-classical' model, are necessary for the covariant formulation. The dynamical term for these extra variables is naturally obtained and the meaning of the constraint term $p^\s\L_{\s\n}+mt_\n =0$, which was recently shown to give `quasi-supersymmetry', is clarified.