Relativistic Particles Coupled to Chern-Simons Term-Revisited

Abstract

We consider the model of N relativistic spinless particles coupled to an abelian Chern-Simons term. Rewriting the action in a time reparametrized form by introducing an arbitrary parameter, parametrizing the world line of the particles, we make a classical constraint Hamiltonian analysis of the model. Subsequent to gauge fixing by equating the arbitrary parameter with time we identify the Hamiltonian of the system, which agrees with the Hamiltonian obtained by using Banerjee′s method of fixing the arbitrary Lagrange multiplier by using equations of motion. We exhibit the Poincaré invariance of the model, at the classical level, by constructing spacetime generators using either the canonical or symmetric definition of the energy-momentum tensor. A detailed comparison of the expressions of angular momentum obtained by both methods shows that both agree up to a boundary term. In presence of a rotationally symmetric vortex configuration this term can be interpreted as an anomalous angular momentum term. We also heuristically discuss the effect of gauge fixing on the transformation properties.