QUANTIZATIONS OF THE FERMION-COUPLED CP1 MODEL WITH THE CHERN-SIMONS TERM - STATISTICS TRANSMUTATION IN COMMUTATOR ALGEBRA

We consider the CP1 model with the Chern-Simons term coupled to a fermion, which is a possible model of the high-T(c) superconductivity. By using the Dirac algorithm, we construct the generalized Hamiltonian formalism for this system and quantize it canonically. The path-integral quantization is also performed following the Faddeev-Senjanovic procedure. On the basis of the quantized system, we show that the bose-fermi transmutation of each field content occurs, by investigating the equal-time (anti-) commutators.