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

Abstract

$\mathrm{SU}(2|1)$ 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 $\mathrm{U}(2)$ spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra $\widehat{su}(2|1)$. The full system admits an $\mathrm{SU}(2|1)$ covariant separation into the center-of-mass sector and the quotient. We derive explicit expressions for the classical and quantum $\mathrm{SU}(2|1)$ 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.

1+35 pages, v2: introduction extended, minor changes, published version

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Cited by in corpus (13)

• $\mathcal{N}$-extended supersymmetric Calogero models
• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• Supersymmetric many-body Euler-Calogero-Moser model
• Multiparticle $\mathcal{N}=8$ mechanics with $F(4)$ superconformal symmetry
• Deformed $\mathcal{N}=8$ mechanics of $(8,8,0)$ multiplets
• $\mathcal{N}=2$ supersymmetric hyperbolic Calogero-Sutherland model
• Supersymmetric V-systems
• Superfield approach to higher derivative N=1 superconformal mechanics
• A three-dimensional superconformal quantum mechanics with $sl(2|1)$ dynamical symmetry
• SU$(2|1)$ supersymmetric spinning models of chiral superfields
• $\mathcal{N}=4$ supersymmetric $\mathrm{U}(2)$-spin hyperbolic Calogero-Sutherland model
• New $\mathcal{N}=2$ superspace Calogero models
• Supersymmetric Calogero models from superfield gauging