Relativistic Spinning Particle in a Non-Commutative Extended Spacetime

TL;DR

This paper analyzes a relativistic spinning particle model in an extended, non-commutative spacetime, revealing a novel non-commutative structure that encodes spin effects through gauge fixing and Hamiltonian analysis.

Contribution

It introduces a Hamiltonian analysis of a spinning particle in an extended space, uncovering a new non-commutative algebra that captures spin dynamics.

Findings

Discovered a non-commutative phase space structure.

Showed the non-commutative algebra encodes spin effects.

Simplified the model via gauge fixing for further analysis.

Abstract

The relativistic spinning particle model, proposed in [3,4], is analyzed in a Hamiltonian framework. The spin is simulated by extending the configuration space by introducing a light-like four vector degree of freedom. The model is heavily constrained and constraint analysis, in the Dirac scheme, is both novel and instructive. Our major finding is an associated novel non-commutative structure in the extended space. This is obtained in a particular gauge. The model possesses a large gauge freedom and hence a judicious choice of gauge becomes imperative. The gauge fixed system in reduced phase space simplifies considerably for further study. We have shown that this non-commutative phase space algebra is essential in revealing the spin effects in the particle model through the Lorentz generator and Hamiltonian equations of motion.