Deformed "Commutative" Chern - Simons System

TL;DR

This paper investigates a noncommutative Chern-Simons system, revealing a deformed 'commutative' phase space where calculations resemble the classical case, and provides spectra of energy and angular momentum at the full deformed level.

Contribution

It introduces a full deformed analysis of the noncommutative Chern-Simons system and identifies a deformed 'commutative' phase space through a non-canonical transformation.

Findings

Spectra of energy and angular momentum are obtained at the full deformed level.

A deformed 'commutative' phase space is identified, simplifying calculations.

The noncommutative-commutative correspondence is explicitly demonstrated.

Abstract

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 the 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.