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

TL;DR

This paper develops an $ ext{SU}(2|1)$ supersymmetric quantum model with spin degrees of freedom, providing explicit generators, spectra, and state analysis, advancing understanding of supersymmetric Calogero-Moser systems.

Contribution

It introduces an $ ext{N}=4$ supersymmetrization of the spin Calogero-Moser model with an intrinsic mass parameter from a centrally-extended superalgebra.

Findings

Explicit classical and quantum $ ext{SU}(2|1)$ generators derived.

Energy spectra and degeneracies determined.

System admits a covariant separation into center-of-mass and quotient sectors.

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.