Super-Calogero model with OSp(2|2) supersymmetry : is the construction unique?
arXiv:hep-th/0309183 · doi:10.1016/j.nuclphysb.2003.12.011
Abstract
We show that the construction of super-Calogero model with OSp(2|2) supersymmetry is not unique. In particular, we find a new co-ordinate representation of the generators of the OSp(2|2) superalgebra that appears as the dynamical supersymmetry of the rational super-Calogero model. Both the quadratic and the cubic Casimir operators of the OSp(2|2) are necessarily zero in this new representation, while they are, in general, nonzero for the super-Calogero model that is currently studied in the literature. The Scasimir operator that exists in the new co-ordinate representation is not present in the case of the existing super-Calogero model. We also discuss the case of N free superoscillators and superconformal quantum mechanics for which the same conclusions are valid.
Revtex4, 20 pages, no figure; Version to appear in Nuclear Physics B
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