Algebra of one-particle operators for the Calogero model

Abstract

An algebra $\mathcal{G}$ of symmetric {\em one-particle} operators is constructed for the Calogero model. This is an infinite-dimensional Lie-algebra, which is independent of the interaction parameter $\lambda$ of the model. It is constructed in terms of symmetric polynomials of raising and lowering operators which satisfy the commutation relations of the $S_N$-{\em extended} Heisenberg algebra. We interpret $\mathcal{G}$ as the algebra of observables for a system of identical particles on a line. The parameter $\lambda$, which characterizes (a class of) irreducible representations of the algebra, is interpreted as a statistics parameter for the identical particles.

23 pages, LaTeX

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Cited by in corpus (11)

• Supersymmetry, Shape Invariance and Solvability of $A_{N-1}$ and $B{C}_N$ Calogero-Sutherland Model
• Dynamical symmetry algebra of the Calogero model
• From Vertex Operators to Calogero-Sutherland Models
• Finite Chern-Simons matrix model - algebraic approach
• Algebra of the observables in the Calogero model and in the Chern-Simons matrix model
• Dunkl symplectic algebra in generalized Calogero models
• Algebra of Observables for Identical Particles in One Dimension
• Anyons, Deformed Oscillator Algebras and Projectors
• A Casimir operator for a Calogero $W$ algebra
• Generalized statistics and the algebra of observables
• Dynamical symmetries of the Calogero-Coulomb model