Deformed Heisenberg algebra, fractional spin fields, and supersymmetry without fermions

Within a group-theoretical approach to the description of (2 + 1)-dimensional anyons, the minimal covariant set of linear differential equations is constructed for the fractional spin fields with the help of the deformed Heisenberg algebra (DHA), [a(-), a(+)] = 1 + nu K, involving the Klein operator K, {K, a(+/-)} = 0, K-2 = 1. The connection of the minimal set of equations with the earlier proposed ''universal'' vector set of anyon equations is established. On the basis of this algebra, a bosonization of supersymmetric quantum mechanics is carried out. The construction comprises the cases of exact and spontaneously broken N = 2 supersymmetry allowing us to realize a Bose-Fermi transformation and spin-1/2 representation of SU(2) group in terms of one bosonic oscillator. The construction admits an extension to the case of OSp(2\2) supersymmetry, and, as a consequence, both applications of the DHA turn out to be related. The possibility of ''superimposing'' the two applications of the DHA for constructing a supersymmetric (2+1)-dimensional anyon system is discussed. As a consequential result we point out that the osp(2\2) superalgebra is realizable as an operator algebra for a quantum mechanical 2-body (nonsupersymmetric) Calogero model. (C) 1996 Academic Press, Inc.