ANYONS AND CHERN–SIMONS THEORY ON COMPACT SPACES OF FINITE GENUS

We study the coupling of an abelian Chern–Simons field to fermions in space–times of the form R × M², where M² is a compact riemannian manifold. Upon integrating out the non-zero modes of the Chern–Simons field, an effective N-particle hamiltonian is constructed, which involves a term representing the effects of the zero modes. We also study the transformation to the fractional statistics (anyon) basis. It is shown that unlike the case of the flat euclidean M² the anyon wave equation involves some residual metric dependent interactions, and the wave function is multivalued.