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arXiv · 1801.00206

Quantum SU(2$|$1) supersymmetric Calogero-Moser spinning systems

Sergey Fedoruk·Evgeny Ivanov·Olaf Lechtenfeld·Stepan Sidorov
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Abstract

${\rm SU}(2|1)$ supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an $\mathcal{N}{=}\,4$ supersymmetrization of the quantum ${\rm U}(2)$ spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra $\widehat{su}(2|1)$. The full system admits an ${\rm SU}(2|1)$ covariant separation into the center-of-mass sector and the quotient. We derive explicit expressions for the classical and quantum ${\rm SU}(2|1)$ generators in both sectors as well as for the total system, and we determine the relevant energy spectra, degeneracies, and the sets of physical states.

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Sergey Fedoruk, Evgeny Ivanov, Olaf Lechtenfeld, Stepan Sidorov. 2018-04-09. Quantum SU(2$|$1) supersymmetric Calogero-Moser spinning systems. https://doi.org/10.1007/jhep04(2018)043

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