A Generalized Model for the Classical Relativistic Spinning Particle

TL;DR

This paper develops a comprehensive Lagrangian framework for relativistic spinning particles based on Poincare algebra, revealing oscillatory solutions and clarifying the gauge structure of the system.

Contribution

It introduces a generalized set of Lagrangians for relativistic spinning particles derived from Poincare algebra Casimirs, extending previous models.

Findings

Oscillatory solutions representing spinning motion

Systematic construction of Lagrangians from algebraic principles

Identification of the correct gauge for spinning dynamics

Abstract

Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the Lagrangian given in the literature. Then we analyze the dynamics of this generalized system in the Lagrangian formulation and show that the equations of motion support an oscillatory solution corresponding to the spinning nature of the system. Next we analyze the canonical structure of the system and present the correct gauge suitable for the spinning motion of the system.