The perturbation of the quantum Calogero-Moser-Sutherland system and related results
Quantum Algebra
2009-10-31 v2 High Energy Physics - Theory
Spectral Theory
Exactly Solvable and Integrable Systems
Abstract
The Hamiltonian of the trigonometric Calogero-Sutherland model coincides with some limit of the Hamiltonian of the elliptic Calogero-Moser model. In other words the elliptic Hamiltonian is a perturbed operator of the trigonometric one. In this article we show the essential self-adjointness of the Hamiltonian of the elliptic Calogero-Moser model and the regularity (convergence) of the perturbation for the arbitrary root system. We also show the holomorphy of the joint eigenfunctions of the commuting Hamiltonians w.r.t the variables (x_1, >..., x_N) for the A_{N-1}-case. As a result, the algebraic calculation of the perturbation is justified.
Keywords
Cite
@article{arxiv.math/0009244,
title = {The perturbation of the quantum Calogero-Moser-Sutherland system and related results},
author = {Yasushi Komori and Kouichi Takemura},
journal= {arXiv preprint arXiv:math/0009244},
year = {2009}
}
Comments
Revised version, 35 pages