Super-Calogero model with OSp(2|2) supersymmetry : is the construction unique?
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.
Keywords
Cite
@article{arxiv.hep-th/0309183,
title = {Super-Calogero model with OSp(2|2) supersymmetry : is the construction unique?},
author = {Pijush K. Ghosh},
journal= {arXiv preprint arXiv:hep-th/0309183},
year = {2010}
}
Comments
Revtex4, 20 pages, no figure; Version to appear in Nuclear Physics B