A Maxwell-Chern-Simons model of a collectively interacting particle system

We propose a new nonrelativistic abelian Maxwell-Chern-Simons model describing a collectively interacting particle system obeying a generalized Exclusion-Inclusion Principle. Starting from the Lagrangian of the system, in the frame of the canonical formalism, we derive the equations of motion for matter and gauge fields. Within this model we write and study the Ehrenfest relations. Finally, we show that the energy of the system is limited at the lower boundary, independent of the value of the parameter which quantifies the action of the Exclusion-Inclusion Principle.