Deformed supersymmetric quantum mechanics with spin variables

TL;DR

This paper quantizes a deformed supersymmetric quantum mechanics model with spin variables, revealing its energy spectrum, supermultiplet structure, and hidden superconformal symmetry ${ m OSp}(4|2)$, unifying states into irreducible multiplets.

Contribution

It introduces a quantization of a deformed supersymmetric model with spin degrees of freedom, uncovering its supermultiplet structure and hidden superconformal symmetry.

Findings

States form irreducible multiplets of ${ m SU}(2|1)$.

The model exhibits hidden ${ m OSp}(4|2)$ superconformal symmetry.

Physical states are unified into irreducible ${ m OSp}(4|2)$ multiplets.

Abstract

We quantize the one-particle model of the ${\rm SU}(2|1)$ supersymmetric multi-particle mechanics with the additional semi-dynamical spin degrees of freedom. We find the relevant energy spectrum and the full set of physical states as functions of the mass-dimension deformation parameter $m$ and ${\rm SU}(2)$ spin $q \in \big( \mathbb{Z}_{>0}\,$, $1/2 + \mathbb{Z}_{\geqslant 0}\big)\,$. It is found that the states at the fixed energy level form irreducible multiplets of the supergroup ${\rm SU}(2|1)\,$. Also, the hidden superconformal symmetry ${\rm OSp}(4|2)$ of the model is revealed in the classical and quantum cases. We calculate the ${\rm OSp}(4|2)$ Casimir operators and demonstrate that the full set of the physical states belonging to different energy levels at fixed $q$ are unified into an irreducible ${\rm OSp}(4|2)$ multiplet.