Intertwining relations for the matrix Calogero-like models: supersymmetry and shape invariance

2002/08/20 by M. V. Ioffe, M V Ioffe, A I Neelov +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/0305-4470/35/35/306

published as J.Phys.A35:7613-7628,2002 · 24 p.p

openalex publication_date 2002/08/20 · arxiv created 2002/09/13 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We investigate the intertwining relations for N -particle Calogero-like models with internal degrees of freedom. Starting from the well-known Dunkl–Polychronakos operators, we construct a new type of local (without exchange operation) differential operator. These operators intertwine the matrix Hamiltonians corresponding to irreducible representations of the permutation group S N . In particular cases, this method allows us to construct a new class of exactly solvable Dirac-like equations and a new class of matrix models with shape invariance. We establish a connection with the approach of multi-dimensional supersymmetric quantum mechanics.

Citations

• Explicit Solution to the N-Body Calogero Problem
• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
• New methods for the two-dimensional Schrödinger equation: SUSY-separation of variables and shape invariance
• Integrable systems for particles with internal degrees of freedom
• Quantum Inozemtsev model, quasi-exact solvability and 𝒩-fold supersymmetry
• Differential-difference operators associated to reflection groups