Deformed supersymmetric quantum mechanics with spin variables

Abstract

We quantize the one-particle model of the $\mathrm{SU}(2|1)$ 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 $\mathrm{SU}(2)$ spin $q\in ({\mathbb{Z}}_{>0}$, $1/2+{\mathbb{Z}}_{⩾0})$. It is found that the states at the fixed energy level form irreducible multiplets of the supergroup $\mathrm{SU}(2|1)$. Also, the hidden superconformal symmetry $\mathrm{OSp}(4|2)$ of the model is revealed in the classical and quantum cases. We calculate the $\mathrm{OSp}(4|2)$ 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 $\mathrm{OSp}(4|2)$ multiplet.

19 pages, 2 figures; v3: comments and new reference added, typos corrected, published version

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• Deformed $\mathcal{N}=8$ mechanics of $(8,8,0)$ multiplets
• A three-dimensional superconformal quantum mechanics with $sl(2|1)$ dynamical symmetry
• On $OSp(N|2)$ superconformal mechanics
• Quantum SU$(2|1)$ supersymmetric ${\mathbb{C}}^N$ Smorodinsky--Winternitz system
• SU$(2|1)$ supersymmetric spinning models of chiral superfields