Deformed “commutative” Chern-Simons' system

Noncommutative Chern-Simons' system is non-perturbatively investigated at a full deformed level. A deformed “commutative” phase space is found by a non-canonical change between two sets of deformed variables of noncommutative space. It is explored that in the “commutative” phase space all calculations are similar to the case in commutative space. Spectra of its energy and angular momentum of the Chern-Simons' system are obtained at the full deformed level. The noncommutative-commutative correspondence is clearly showed. Formalism for the general dynamical system is briefly presented. Some subtle points are clarified.