Super-Calogero model with OSp(2|2) supersymmetry : is the construction unique?

TL;DR

This paper demonstrates that the super-Calogero model with OSp(2|2) supersymmetry admits multiple representations, revealing non-uniqueness in its construction and introducing a new coordinate representation with distinct algebraic properties.

Contribution

The authors present a new coordinate representation of the OSp(2|2) superalgebra for the super-Calogero model, showing that its construction is not unique and exploring implications for related models.

Findings

New coordinate representation of OSp(2|2) generators

Casimir operators are zero in the new representation

Existence of a Scasimir operator in the new representation

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.