Teoria de campos com estatística fracionária

Abstract

In 1988 G. W. Semenoff proposed a theoretical model based on the Chern-Simons term (C.S) for the explicit accomplishment of anyons. Anyons are particles in a (2 + 1) dimensional space involved in the explanation of important phenomena in solid state physics like, for example, the high temperature superconductivity and the fractional quantum Hall effect, among others. Semenoff's model contains, besides the C. S. term, a gauge field Aμ which couples minimally to the matter field ø. ln this dissertation, we investigate further the origin of fractional statistics in the model of Semenoff. We consider, then, models with non-minimal coupling in the search of alternatives for the attainment of fractional statistics. ln these models, the non-minimal term of the coupling is constructed from a field redefinition of the gauge field Aμ. We find, in fact, non-minimal models with such property as well as new aspects previously masked by the minimal coupling. Another form to insert the non-minimal interaction is presented and the sarne results were obtained.