EFFECT OF ROTATION SYMMETRY ON ABELIAN CHERN-SIMONS FIELD-THEORY AND ANYON EQUATION ON A SPHERE

We analyze Chern-Simons field theory coupled to a nonrelativistic matt er field on a sphere using canonical transformation on the fields with special attention to the role of the rotation symmetry: SO(3) invaria nce restricts the Hilbert space to the one with a definite number of c harges and dictates the Dirac quantization condition to the Chern-Simo ns coefficient, whereas SO(2) invariance does not. The corresponding S chrodinger equation for many anyons (and for multispecies) on the sphe re is presented with appropriate boundary conditions. In the presence of an external magnetic monopole source, the ground state solutions of anyons are compared with monopole harmonics. The role of the translat ion and modular symmetry on a torus is also expounded.