Quantal Symmetries in the Nonlinear Sigma Model with Maxwell–Chern–Simons Term

The quantal symmetry property in the CP¹ nonlinear sigma model with Abelian–Maxwell–Chern–Simons (AMCS) term in 2 + 1 dimensions is studied. In the Coulomb gauge, the system is quantized in the Faddeev–Senjanovic (FS) path-integral formalism. The canonical Ward identities for proper vertices under local gauge transformation are derived. Based on the quantal symmetries of a constrained Hamiltonian system, the fractional spin at the quantum level of this system is also presented as those of the system without Maxwell term.