Time level splitting in quantum Chern Simons gravity

Using the Dirac theory of constraints, the reduction procedure for the field degrees of freedom, the number of which is restricted by the equations of motion and topological conditions, is proposed. Such a procedure is applied to the Chern Simons gravity generalized by the inclusion of a source, in the case when the space has a torus topology. The splitting of the discrete levels of time due to the presence of additional interaction is observed.