Abstract
Starting from the U (1)× U (1) classical gauge model for the nonrelativistic electromagnetic interaction of anyons, the quantum formalism is constructed. This gauge model containing the statistical U(1) field and 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 field, and we carry out the canonical quantization by following the Dirac formalism. Later on, the path integral approach is developed and the diagrammatic and Feynman rules, in the framework of the perturbation theory, are discussed. Finally, as an alternative method, the BRST formalism for this gauge model is also treated.
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