Chern-Simons theories on the noncommutative plane - art. no. 030402

We investigate U(N) Chern-Simons theories on the noncommutative plane. We s how that for the theories to be consistent quantum mechanically, the coeffi cient of the Chern-Simons term should be quantized kappa = n/2 pi with an i nteger n. This is a surprise for the U(1) gauge theory. When uni form backg round charge density rho (e) is present, the quantization rule changes to k appa + rho (e)theta = n/2 pi with the noncommutative parameter theta. With the exact expression for the angular momentum, we argue in the U(1) theory that charged particles in the symmetric phase carry fractional spin 1/2n an d vortices in the broken phase carry half-integer or integer spin -n/2.