Quantization and conformal properties of a generalized Calogero model

2006/09/22 by B. Basu-Mallick, Stjepan Meljanac, K. S. Gupta +4 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Conformal map #Conformal symmetry #Fock space #Generalization #Geometry #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Realization (probability) #Symmetry (geometry) #Theoretical physics #hep-th

paper · pdf · doi:10.1140/epjc/s10052-006-0163-9

published as Eur.Phys.J.C49:875-889,2007 · 21 pages, revtex4, 4 figures, typos corrected, references added

arxiv created 2006/09/22 · openalex publication_date 2007/01/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We analyze a generalization of the quantum Calogero model with the underlying conformal symmetry, paying special attention to the two-body model deformation. Owing to the underlying SU(1,1) symmetry, we find that the analytic solutions of this model can be described within the scope of the Bargmann representation analysis and we investigate its dynamical structure by constructing the corresponding Fock space realization. The analysis from the standpoint of supersymmetric quantum mechanics (SUSYQM), when applied to this problem, reveals that the model is also shape invariant. For a certain range of the system parameters, the two-body generalization of the Calogero model is shown to admit a one-parameter family of self-adjoint extensions, leading to inequivalent quantizations of the system.

Citations

• Realization of the annihilation operator for generalized oscillator-like system by a differential operator
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Cited by

• Inequivalent Quantization in the Field of a Ferromagnetic Wire