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arXiv · 2603.21325

Dynamical symmetries of the Calogero-Coulomb model

Tigran Hakobyan
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Abstract

We construct the dynamical symmetry of the quantum Calogero model with particle exchange in a confining Coulomb field. This symmetry is governed by the algebra $so(N+1,2)$, deformed by exchange (Dunkl) operators, with its invariant sector generated by the Dunkl angular momentum tensor and the modified Laplace-Runge-Lenz vector. The equidistant analogue of the Hamiltonian, with a linear spectrum, is expressed in terms of the conformal subalgebra $so(1,2)$. In addition, the wave functions of the Calogero-Coulomb Hamiltonian are classified into infinite-dimensional lowest-weight $so(1,2)$ multiplets.

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Tigran Hakobyan. 2026-03-22. Dynamical symmetries of the Calogero-Coulomb model. https://doi.org/10.1016/j.nuclphysb.2026.117522

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