Relativistic Spinning Particle in a Non-Commutative Extended Spacetime

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.