1996/01/23 by Mikhail S. Plyushchay
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1006/aphy.1996.0012
published as Annals Phys. 245 (1996) 339-360 · 21 pages, LaTeX
arxiv created 1996/01/23 · arxiv updated 2009/11/30
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+νK, involving the Klein operator K, \K,a±\=0, K2=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\vert2) supersymmetry, and, as a consequence, both applications of the DHA turn out to be related. A 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 osp(2|2) superalgebra is realizable as an operator algebra for a quantum mechanical 2-body (nonsupersymmetric) Calogero model.