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.