New gauge-invariant formulation of the Chern-Simons gauge theory

A new gauge invariant formulation of the relativistic scalar field interacting with Chern-Simons gauge fields is considered. This formulation is consistent with the gauge fixed formulation. Furthermore, we find that canonical (Noether) Poincaré generators are not gauge invariant even on the constraints surface and do not satisfy the (classical) Poincaré algebra. It is the improved generators, constructed from the symmetric energy-momentum tensor, which are (manifestly) gauge invariant and obey the classical Poincaré algebra.