ANYON EQUATION ON A TORUS

Starting from the quantum field theory of nonrelativistic matter on a torus interacting with Chem-Simons gauge fields, we derive the Schrodinger equation for an anyon system. The nonintegrable phases of the Wilson line integrals on a torus play an essential role. In addition to generating degenerate vacua, they enter in the definition of a many-body Schrodinger wave function in quantum mechanics, which can be defined as a regular function of the coordinates of anyons. It obeys a non-Abelian representation of the braid group algebra, being related to Einarsson's wave function by a singular gauge transformation.