Quantum symmetry of a Chern-Simons system coupled to a polaron

The property of fractional spin of the system with Chern-Simons (CS) term coupled to polaron at the quantum level is studied. According to the rule of path integral quantization for constrained Hamiltonian system in Faddeev-Senjanovic (FS) scheme, this system is quantized. Based on the quantal Noether theorem, the quantal conserved angular momentum and the fractional spin at the quantum level of this system is presented. The fractional spin is also presented in the system including Maxwell kinetic term.