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.

arXiv comment18 pages, no figures

References in corpus (28)

• Exchange Operator Formalism for Integrable Systems of Particles
• Yang-Baxter equation in spin chains with long range interactions
• Physics and Mathematics of Calogero particles
• Explicit Solution to the N-Body Calogero Problem
• Lattice Integrable Systems of Haldane-Shastry Type
• Hidden symmetries of integrable conformal mechanical systems
• Invariants of the Haldane-Shastry $SU(N)$ Chain
• Elliptic quantum many-body problem and double affine Knizhnik-Zamolodchikov equation
• Hidden symmetry of the quantum Calogero-Moser system
• On Dunkl angular momenta algebra
• The quantum angular Calogero-Moser model
• Integrals of motion of the Haldane Shastry Model
• Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
• Nonlinear supersymmetry in the quantum Calogero model
• Hidden algebra of the $N$-body Calogero problem
• Quantum Lax pairs via Dunkl and Cherednik operators
• Runge-Lenz vector in Calogero-Coulomb problem
• Representations of the $S_N$-Extended Heisenberg Algebra and Relations Between Knizhnik-Zamolodchikov Equations and Quantum Calogero Model
• Spherical Calogero model with oscillator/Coulomb potential: quantum case
• Algebra of one-particle operators for the Calogero model
• The structure of invariants in conformal mechanics
• Relationship Between the Energy Eigenstates of Calogero-Sutherland Models With Oscillator and Coulomb-like Potentials
• From fermionic spin-Calogero-Sutherland models to the Haldane-Shastry chain by freezing
• Dunkl symplectic algebra in generalized Calogero models
• Conserved charges of non-yangian type for the Frahm-Polychronakos spin chain
• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
• On symmetries of generalized Calogero model and Polychronakos-Frahm chain
• A Casimir operator for a Calogero $W$ algebra