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Abstract: Universal vector wave equations allowing for a unified description of anyons,and also of usual bosons and fermions in the plane are proposed. The existenceof two essentially different types of anyons, based on unitary and also onnon-unitary infinite-dimensional half-bounded representations of the 2+1DLorentz algebra is revealed. Those associated with non-unitary representationsinterpolate between bosons and fermions. The extended formulation of the theoryincludes the previously known Jackiw-Nair JN and Majorana-Dirac MDdescriptions of anyons as particular cases, and allows us to compose bosons andfermions from entangled anyons. The theory admits a simple supersymmetricgeneralization, in which the JN and MD systems are unified in N=1 and N=2supermultiplets. Two different non-relativistic limits of the theory areinvestigated. The usual one generalizes Levy-Leblond-s spin 1-2 theory toarbitrary spin, as well as to anyons. The second -Jackiw-Nair- limit thatcorresponds to Inonu-Wigner contraction with both anyon spin and light velocitygoing to infinity, is generalized to boson-fermion fields and interpolatinganyons. The resulting exotic Galilei symmetry is studied in both thenon-supersymmetric and the supersymmetric cases.

Autor: Peter A. Horvathy, Mikhail S. Plyushchay, Mauricio Valenzuela


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