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

References in corpus (6)

• Supersymmetric Calogero models by gauging
• Gauging N=4 supersymmetric mechanics II: (1,4,3) models from the (4,4,0) ones
• OSp(4|2) Superconformal Mechanics
• Gauged spinning models with deformed supersymmetry
• Supersymmetric Kähler oscillator in a constant magnetic field
• Gauge and matter superfield theories on $S^2$