NONRELATIVISTIC QUANTUM FORMALISM FOR ELECTROMAGNETIC-INTERACTION OF ANYONS IN THE U(1)XU(1) GAUGE-MODEL

Starting from the U(1) x U(1) classical gauge model for the nonrelativ istic electromagnetic interaction of anyons, the quantum formalism is constructed. This gauge model containing the statistical U(1) field an d the electromagnetic field can be coupled to both, a commuting or an anticommuting matter field. We explicitly consider the second case, i. e. a fermionic anyon system in the presence of an electromagnetic fiel d, and we carry out the canonical quantization by following the Dirac formalism. Later on, the path integral approach is developed and the d iagrammatic and Feynman rules, in the framework of the perturbation th eory, are discussed. Finally, as an alternative method, the BRST forma lism for this gauge model is also treated.