Integrable extensions of the rational and trigonometric $A_N$ Calogero Moser potentials

Abstract

We describe the $R$-matrix structure associated with integrable extensions, containing both one-body and two-body potentials, of the $A_N$ Calogero-Moser $N$-body systems. We construct non-linear, finite dimensional Poisson algebras of observables. Their $N\to \infty$ limit realize the infinite Lie algebras Sdiff$(\mathbb{R}\times S_1)$ in the trigonometric case and Sdiff$({\mathbb{R}}^2)$ in the rational case. It is then isomorphic to the algebra of observables constructed in the two-dimensional collective string field theory.

15 pages; LaTeX; PAR LPTHE 93-23 Revised version including extensive modifications in the demonstrations and the references

References in corpus (4)

• Classical R-matrix structure for the Calogero model
• Algebraic Structures and Eigenstates for Integrable Collective Field Theories
• New Integrable Systems from Unitary Matrix Models
• Scattering States and Symmetries in the Matrix Model and Two Dimensional String Theory

Cited by in corpus (3)

• Observable algebra for the rational and trigonometric Euler Calogero Moser models
• Spherical Calogero model with oscillator/Coulomb potential: classical case
• Totally classical Calogero model