NEW GAUGE INVARIANT FORMULATION OF THE CHERN-SIMONS GAUGE THEORY: CLASSICAL AND QUANTAL ANALYSIS

A recently proposed new gauge invariant formulation of the Chern-Simons gauge theory is considered in detail. This formulation is consistent with the gauge fixed formulation. Furthermore, it is found that the canonical (Noether) Poincare generators are not gauge invariant even on the constraints surface and do not satisfy the Poincare algebra contrast to usual case. It is the improved generators, constructed from the symmetric energy-momentum tensor, which are (manifestly) gauge invariant and obey the quantum as well as classical Poincare algebra. The physical states are constructed and it is found in the Schrodinger picture that unusual gauge invariant longitudinal mode of the gauge field is crucial for constructing the physical wave-functional which is genuine to (pure) Chern-Simons theory. In matching to the gauge fixed formulation, we consider three typical gauges, Coulomb, axial and Weyl gauges as explicit examples. Furthermore, recent several confusions about the effect of Dirac's dressing function and the gauge fixings are clarified. The analysis according to old gauge independent formulation a la Dirac is summarized in an appendix.