Observable algebra for the rational and trigonometric Euler Calogero Moser models

Abstract

We construct polynomial Poisson algebras of observables for the classical Euler-Calogero-Moser (ECM) models. The conserved Hamiltonians and symmetry algebras derived in a previous work are subsets of these algebras. We define their linear, $N\to \infty$ limits, realizing $\w_{\infty}$ type algebras coupled to current algebras.

11 pages; Latex; PAR LPTHE 94-16 Misprints and minor mistakes corrected; references updated

References in corpus (7)

• Exchange Operator Formalism for Integrable Systems of Particles
• Yang-Baxter equation in spin chains with long range interactions
• Integrable Systems for Particles with Internal Degrees of Freedom
• The R-matrix structure of the Euler-Calogero-Moser model
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Cited by in corpus (7)

• The spherical sector of the Calogero model as a reduced matrix model
• Collective field theory of the matrix-vector model
• The Classical $r$-Matrix for the Relativistic Ruijsenaars-Schneider System
• Yangian-invariant field theory of matrix-vector models
• The structure of invariants in conformal mechanics
• Spherical Calogero model with oscillator/Coulomb potential: classical case
• Poisson Structures of Calogero-Moser and Ruijsenaars-Schneider Models