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arXiv · 1710.02130

Deformed supersymmetric quantum mechanics with spin variables

Sergey Fedoruk·Evgeny Ivanov·Stepan Sidorov
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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.

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Sergey Fedoruk, Evgeny Ivanov, Stepan Sidorov. 2017-10-05. Deformed supersymmetric quantum mechanics with spin variables. https://doi.org/10.1007/jhep01(2018)132

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