Deformed Heisenberg Algebra, Fractional Spin Fields, and Supersymmetry without Fermions
✍ Scribed by Mikhail S. Plyushchay
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 385 KB
- Volume
- 245
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
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+&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.