Generalized Calogero model in arbitrary dimensions

Abstract

We define a new multispecies model of Calogero type in D dimensions with harmonic, two-body and three-body interactions. Using the underlying conformal SU(1,1) algebra, we indicate how to find the complete set of the states in Bargmann-Fock space. There are towers of states, with equidistant energy spectra in each tower. We explicitely construct all polynomial eigenstates, namely the center-of-mass states and global dilatation modes, and find their corresponding eigenenergies. We also construct ladder operators for these global collective states. Analysing corresponding Fock space, we detect the universal critical point at which the model exhibits singular behavior. The above results are universal for all systems with underlying conformal SU(1,1) symmetry.

14 pages, no figures, to be published in Phys.Lett.B

References in corpus (24)

• Exchange Operator Formalism for Integrable Systems of Particles
• Exact operator solution of the Calogero-Sutherland model
• Black Holes and Calogero Models
• Explicit Solution to the N-Body Calogero Problem
• Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics
• Near-Horizon Conformal Structure of Black Holes
• The Calogero Model - Anyonic Representation, Fermionic Extension and Supersymmetry
• Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators
• Analytic results for $N$ particles with $1/r^2$ interaction in two dimensions and an external magnetic field
• A Quantum Many-body Problem in Two Dimensions: Ground State
• Novel correlations in two dimensions: Some exact solutions
• A multispecies Calogero model
• A multispecies Calogero-Sutherland model
• Calogero-Sutherland Type Models in Higher Dimensions
• Extended superconformal symmetry and Calogero-Marchioro model
• Calogero model, deformed oscillators and the collapse
• Permutation Invariant Algebras, a Fock Space Realization and the Calogero Model
• Exactly Solvable Models in Arbitrary Dimensions
• Calogero Models for Distinguishable Particles
• Degeneracy Structure of the Calogero-Sutherland Model: an Algebraic Approach
• A Unified Algebraic Approach to Few and Many-Body Correlated Systems
• Towards a quantum-mechanical model for multispecies exclusion statistics
• Novel classical ground state of a many body system in arbitrary dimensions
• Microscopic analytical theory of a correlated, two-dimensional N-electron gas in a magnetic field

Cited by in corpus (14)

• Remark on quantum mechanics with N=2 Schrodinger supersymmetry
• Quantization and Conformal Properties of a Generalized Calogero Model
• Truncated Calogero-Sutherland models
• Supersymmetric Extensions of Calogero--Moser--Sutherland like Models: Construction and Some Solutions
• Universal properties of conformal quantum many-body systems
• Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
• Quantized Normal Matrices: Some Exact Results and Collective Field Formulation
• Superconformal Quantum Mechanics via Wigner-Heisenberg Algebra
• Waves and Solitons in the Calogero Model - Revisited
• Inequivalent quantization of the rational Calogero model with a Coulomb type interaction
• Thermodynamics of Statistical Anyons
• Matrix oscillator and Laughlin Hall states
• Taxonomy of integrable and ground-state solvable models: Jastrow wave functions on graphs and parent Hamiltonians
• Calogero Model(s) and Deformed Oscillators