Relativistic spinning particle in a noncommutative extended spacetime

The relativistic spinning particle model, proposed in [S. M. Kuzenko, S. L. Lyakhovich, and A. Y. Segal, Int. J. Mod. Phys. A 10, 1529 (1995); A. Staruszkiewicz, Acta Phys. Pol. A 1, 109 (2008).] is analyzed in a Hamiltonian framework. The spin is simulated by extending the configuration space by introducing a lightlike 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 noncommutative 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 noncommutative phase space algebra is essential in revealing the spin effects in the particle model through the Lorentz generator and Hamiltonian equations of motion.