A Maxwell–Chern–Simons model for a quantum system obeying an exclusion–inclusion principle

In this paper we generalize a canonical model, recently proposed by us [Phys. Rew. E 58 (1998) 5574 and Phys. A 255 (1998) 474], describing a quantum system of particles obeying to a exclusion–inclusion principle. In the new model the system is coupled in a minimal fashion with an Abelian gauge field whose interaction is described in the frame of the Maxwell–Chern–Simons picture. The Lagrangian and Hamiltonian formulations of the model are considered and the Ehrenfest relations are obtained. The main symmetries and the related conserved quantities of the model are studied. Finally, the statistical behavior of the system is discussed.