CHERN-SIMONS QUANTUM-MECHANICS

The author considers the quantum mechanics coupled to the gauge field which has the Chern-Simons term as the action. The generalized Hamiltonian formalism of the system is constructed and canonical and path-integral quantizations are performed. In solving the Gauss law constraint, the gauge field is represented by a multivalued function and the charge density operator of the particle. The gauge potential is singular and also induces a singular magnetic field through the magnetic flux is finite. By a phase transformation, the singular gauge field is eliminated. Then the transformed wavefunction absorbing the gauge field induces a novel phase factor under 2 pi -rotation in space. Thus the author shows that the transformed wavefunction describes exotic spin state. The extension of these analyses to the relativistic case is also presented.