PHASE-SPACE STRUCTURE OF NON-ABELIAN CHERN SIMMONS PARTICLES

The classical phase space structure of N SU(n + 1) non-Abelian Chem-Si mons (NACS) particles is investigated by first constructing the produc t space of associated SU(n + 1) bundle with CP(n) as the fiber. The Po isson bracket is calculated using the symplectic structure on the asso ciated bundle and it is found that the minimal substitution in the pre sence of external gauge fields is equivalent to the modification of sy mplectic structure by the addition of field strength two form. Then, a direct product of the associated bundle is taken by the space of all connections and a specific connection is chosen by the condition of va nishing momentum map corresponding to the gauge transformation, thus r ecovering the quantum mechanical model of NACS particles in Lee and Oh [Phys. Rev. Lett. 72, 1141 (1994)].