Symmetries In Constrained System And Their Applications To Chern-Simons Theories

Quantization of the constrained Hamiltonian system is very briefly reviewed. The canonical Ward identities and the quantal conserved laws for global symmetry transformations have been discussed for the case when path-integral measure is not invariant under global transformations. Applying to Maxwell-Chern-Simons theory the canonical Ward identities and the quantal conserved laws have been obtained. Based on the configuration-space generating function of Green function, Ward identities for non- local transformation have been derived. The application of the results to the non-Abelian Chern-Simons term coupled to fermionic field, the Ward identities for the gauge-ghost field proper vertices have been also deduced. The other form of Ward identities and the quantal conserved laws for global symmetry transformations in configuration-space have been discussed for the case when path-integral measure is not invariant under the corresponding transformation. Applying to Maxwell-Chern-Simons theory the results are obtained which agree with those in phase-space path integeral. The composite operator has been constructed and investigated with respect to the Maxwell-Chern-Simons theory as well as Non-Abelian Chern-Simons theory. Finally the fractional spin term for those systems is obtained by computing the angular momentum.