Related papers: Dynamical symmetries of the Calogero-Coulomb model

Dynamical symmetries of the Calogero-Coulomb model

URL: http://arxiv.org/abs/2603.21325v1
Date: Sun, 22 Mar 2026 17:09:21 GMT
Title: Dynamical symmetries of the Calogero-Coulomb model
Abstract summary: We construct the dynamical symmetry of the quantum Calogero model with particle exchange in a confining Coulomb field.<n>This symmetry is governed by the algebra $so(N+1,2)$, deformed by exchange (Dunkl) operators.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
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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