Algebra of the observables in the Calogero model and in the Chern-Simons matrix model

Abstract

The algebra of observables of an N-body Calogero model is represented on the S_N-symmetric subspace of the positive definite Fock space. We discuss some general properties of the algebra and construct four different realizations of the dynamical symmetry algebra of the Calogero model. Using the fact that the minimal algebra of observables is common to the Calogero model and the finite Chern-Simons (CS) matrix model, we extend our analysis to the CS matrix model. We point out the algebraic similarities and distinctions of these models.

24 pages, misprints corrected, reference added, final version, to appear in PRB

References in corpus (11)

• The Quantum Hall Fluid and Non-Commutative Chern Simons Theory
• Quantum Hall states as matrix Chern-Simons theory
• Quantum Hall Physics = Noncommutative Field Theory
• Chern-Simons matrix model: coherent states and relation to Laughlin wavefunctions
• Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials
• Orthogonal basis for the energy eigenfunctions of the Chern-Simons matrix model
• Bosonic realization of algebras in the Calogero model
• Calogero model, deformed oscillators and the collapse
• Permutation Invariant Algebras, a Fock Space Realization and the Calogero Model
• Dynamical symmetry algebra of the Calogero model
• Finite Chern-Simons matrix model - algebraic approach

Cited by in corpus (6)

• Harmonic oscillator with minimal length uncertainty relations and ladder operators
• Noncommutative Quantum Scattering in a Central Field
• A multispecies Calogero model
• Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
• Dunkl symplectic algebra in generalized Calogero models
• Matrix oscillator and Laughlin Hall states