Deformed Heisenberg algebra, fractional spin fields, and supersymmetry without fermions
- Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, Zaragoza 50009 (Spain)
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), [{ital a}{sup {minus}},{ital a}{sup +}]=1+{nu}{ital K}, involving the Klein operator {ital K}, {l_brace}{ital K},{ital a}{sup {plus_minus}}{r_brace}=0, {ital K}{sup 2}=1. The connection of the minimal set of equations with the earlier proposed {open_quote}{open_quote}universal{close_quote}{close_quote} 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 {ital N}=2 supersymmetry allowing us to realize a Bose{endash}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{parallel}2) supersymmetry, and, as a consequence, both applications of the DHA turn out to be related. The possibility of {open_quote}{open_quote}superimposing{close_quote}{close_quote} 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 {ital osp}(2{parallel}2) superalgebra is realizable as an operator algebra for a quantum mechanical 2-body (nonsupersymmetric) Calogero model. Copyright {copyright} 1996 Academic Press, Inc.
- OSTI ID:
- 282865
- Journal Information:
- Annals of Physics (New York), Vol. 245, Issue 2; Other Information: PBD: Feb 1996
- Country of Publication:
- United States
- Language:
- English
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