Calogero models and nonlocal conformal transformations

Abstract

We propose a universal method of relating the Calogero model to a set of decoupled particles on the real line, which can be uniformly applied to both the conformal and nonconformal versions as well as to supersymmetric extensions. For conformal models the simplification is achieved at the price of a nonlocal realization of the full conformal symmetry in the Hilbert space of the resulting free theory. As an application, we construct two different N=2 superconformal extensions.

1+9 pages, v2: tex macros fixed

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Cited by in corpus (39)

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• New D(2,1;alpha) Mechanics with Spin Variables
• N=4 mechanics, WDVV equations and roots
• Remark on quantum mechanics with conformal Galilean symmetry
• Cuboctahedric Higgs oscillator from the Calogero model
• Action-angle variables for dihedral systems on the circle
• Remark on quantum mechanics with N=2 Schrodinger supersymmetry
• Conformal bridge between asymptotic freedom and confinement
• Lobachevsky geometry of (super)conformal mechanics
• Invariants of the spherical sector in conformal mechanics
• Harmonic N=2 Mechanics
• AdS/NRCFT for the (super) Calogero model
• Spherical Calogero model with oscillator/Coulomb potential: quantum case
• N=2 supersymmetric extension of the Tremblay-Turbiner-Winternitz Hamiltonians on a plane
• Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems
• The structure of invariants in conformal mechanics
• Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations
• Lobachevsky geometry in TTW and PW systems
• Remarks on Multi-Dimensional Conformal Mechanics
• Conformal mechanics
• $\mathcal{N}=2$ supersymmetric hyperbolic Calogero-Sutherland model
• Superconformal Quantum Mechanics from M2-branes
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Higher-derivative generalization of conformal mechanics
• Remarks on N=1 supersymmetric extension of the Euler top
• Comments on dihedral and supersymmetric extensions of a family of Hamiltonians on a plane
• Dual multiplets in N=4 superconformal mechanics
• Superfield approach to higher derivative N=1 superconformal mechanics
• New Super Calogero Models and OSp(4|2) Superconformal Mechanics
• Generalizations of MICZ-Kepler system
• On the Schwarzian counterparts of conformal mechanics
• $\mathcal{N}=4$ supersymmetric $\mathrm{U}(2)$-spin hyperbolic Calogero-Sutherland model
• Conformal mechanical treatment of Calogero-Moser model and infinite dimensional Lie algebra of conformal Galilei type
• Superintegrable deformations of oscillator and Coulomb systems