A Covariant Formulation of Classical Spinning Particle

TL;DR

This paper presents a covariant reformulation of classical spinning particles using the Poincaré group, introducing a comprehensive Lagrangian with explicit constraints and revealing a supersymmetry-like symmetry.

Contribution

It develops a covariant Lagrangian framework for spinning particles that explicitly encodes all constraints and aligns with pseudo-classical formulations, enhancing theoretical understanding.

Findings

Explicit covariant Lagrangian with all constraints derived

Lorentz evolution of momentum and spin from arbitrary frames

Discovery of a supersymmetry-like symmetry in the system

Abstract

Covariantly we reformulate the description of a spinning particle in terms of the Poincar\'{e} group. We also construct a Lagrangian which entails all possible constraints explicitly; all constraints can be obtained just from the Lagrangian. Furthermore, in this covariant reformulation, the Lorentz element is to be considered to evolve the momentum or spin component from an arbitrary fixed frame and not just from the particle rest frame. In distinction with the usual formulation, our system is directly comparable with the pseudo-classical formulation. We get a peculiar symmetry which resembles the supersymmetry of the pseudo-classical formulation.