Dynamical symmetries of the Calogero-Coulomb model

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.

18 pages, no figures

References in corpus (6)

• Physics and Mathematics of Calogero particles
• Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
• From fermionic spin-Calogero-Sutherland models to the Haldane-Shastry chain by freezing
• Dunkl symplectic algebra in generalized Calogero models
• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
• A Casimir operator for a Calogero $W$ algebra