MINIMAL BOSONIZATION OF SUPERSYMMETRY

Abstract

The minimal bosonization of supersymmetry in terms of one bosonic degree of freedom is considered. A nontrivial relationship of the construction to the Witten supersymmetric quantum mechanics is illustrated with the help of the simplest N=2 SUSY system realized on the basis of the ordinary (undeformed) bosonic oscillator. It is shown that the generalization of such a construction to the case of Vasiliev deformed bosonic oscillator gives a supersymmetric extension of the two-body Calogero model in the phase of exact or spontaneously broken N=2 SUSY. The construction admits an extension to the case of the OSp(2|2) supersymmetry, and, as a consequence, osp(2|2) superalgebra is revealed as a dynamical symmetry algebra for the bosonized supersymmetric Calogero model. Realizing the Klein operator as a parity operator, we construct the bosonized Witten supersymmetric quantum mechanics. Here the general case of the corresponding bosonized N=2 SUSY is given by an odd function being a superpotential.