Gauge symmetry breaking in gravity and auxiliary effective action

In the context of the covariant symmetry breaking in gravity, we study the quantum aspect of Chamseddine–Mukhanov model by making use of path integral method. Utilizing one of the gauge fixing constraints, we remove the specific ghost degree of freedom. In continuation, we define an auxiliary effective action. Introducing an auxiliary field, we will have a new dynamic field in addition to the fundamental field.

CHERN–SIMONS MECHANICS IN NONCOMMUTATIVE PHASE SPACE

Chern–Simons mechanics in noncommutative phase space is studied from both classical and quantum aspects in this paper. We find that there are two parameters in the full theory which lead to two different reduced theories when they take certain values. We analyze these two reduced models also from two aspects and find that the classical aspect of the full theory has a continuous limit when both of these parameters take their certain values. However, the quantum aspect of the full theory does not have the similar limit. The spectra of the full theory will be infinite when these parameters take these values. We propose artificial regularization schemes to get rid of these infinity and resort to Dirac's theories to verify our scheme.