Common Algebraic Structure for the Calogero-Sutherland Models
نویسنده
چکیده
We investigate common algebraic structure for the rational and trigonometric Calogero-Sutherland models by using the exchange-operator formalism. We show that the set of the Jack polynomials whose arguments are Dunkl-type operators provide an orthogonal basis for the rational case. One dimensional quantum integrable models with long-range interaction have attracted much interest, because of not only their physical significance, but also their beautiful mathematical structure. One of such models is the Sutherland (trigonometric) model, which describes interacting particles on a circle[1]. The total momentum and Hamiltonian of the model are respectively given by
منابع مشابه
The Algebraic Structure of the Gl(n|m) Color Calogero-sutherland Models
We extend the study on the algebraic structure of the su(n) color Calogero-Sutherland models to the case of gl(n|m) color CS model and show that the generators of the super-Yangian Y (gl(n|m)) can be obtained from two gl(n|m) loop algebras. Also, a super W ∞ algebra for the SUSY CS model is constructed.
متن کاملShape Invariance in the Calogero and Calogero-Sutherland Models
We show that the Calogero and Calogero-Sutherland models possess an N -body generalization of shape invariance. We obtain the operator representation that gives rise to this result, and discuss the implications of this result, including the possibility of solving these models using algebraic methods based on this shape invariance. Our representation gives us a natural way to construct supersymm...
متن کاملOn PT-symmetric extensions of the Calogero and Sutherland models
The original Calogero and Sutherland models describe N quantum particles on the line interacting pairwise through an inverse square and an inverse sinussquare potential. They are well known to be integrable and solvable. Here we extend the Calogero and Sutherland Hamiltonians by means of new interactions which are PT-symmetric but not self adjoint. Some of these new interactions lead to integra...
متن کاملar X iv : h ep - t h / 99 10 12 3 v 2 2 6 O ct 1 99 9 Free harmonic oscillators , Jack polynomials and Calogero - Sutherland systems
The algebraic structure and the relationships between the eigenspaces of the Calogero-Sutherland model (CSM) and the Sutherland model (SM) on a circle are investigated through the Cherednik operators. We find an exact connection between the simultaneous non-symmetric eigenfunctions of the AN−1 Cherednik operators, from which the eigenfunctions of the CSM and SM are constructed, and the monomial...
متن کاملar X iv : h ep - t h / 99 10 12 3 v 1 1 5 O ct 1 99 9 Free harmonic oscillators , Jack polynomials and Calogero - sutherland systems
The algebraic structure and the relationships between the eigenspaces of the Calogero-Sutherland model (CSM) and the Sutherland model (SM) on a circle are investigated through the Cherednik operators. We find an exact connection between the simultaneous non-symmetric eigenfunctions of the AN−1 Cherednik operators, from which the eigenfunctions of the CSM and SM are constructed, and the monomial...
متن کامل