PERTURBED CHERN-SIMONS THEORY, FRACTIONAL STATISTICS, AND YANG-BAXTER ALGEBRA

Topological Chern-Simons theory coupled to matter fields is analysed in the frame work of Dirac's method of quantising constrained systems in a general class of linear, non-local gauges. We show that in the weak coupling limit gauge invariant operators in the theory transform under an exchange according to a higher dimensional representation of the braid group which is built out of the fundamental representation matrices of the gauge group and thus behave like anyons. We also discover new solutions of the Yang-Baxter equation which emerges as a consistency condition on the structure functions of the operator algebra of the matter fields.