Poisson Structures of Calogero-Moser and Ruijsenaars-Schneider Models

Abstract

We examine the Hamiltonian structures of some Calogero-Moser and Ruijsenaars-Schneider N-body integrable models. We propose explicit formulations of the bihamiltonian structures for the discrete models, and field-theoretical realizations of these structures. We discuss the relevance of these realizations as collective-field theory for the discrete models.

15 pages, no figures; v2 references added, typos corrected

References in corpus (4)

• On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models
• Multiple Hamiltonian Structures for Toda-type systems
• Notes on Collective Field Theory of Matrix and Spin Calogero Models
• On the superintegrability of the rational Ruijsenaars-Schneider model

Cited by in corpus (4)

• Some connections between the Classical Calogero-Moser model and the Log Gas
• Bi-Hamiltonian structure of spin Sutherland models: the holomorphic case
• Bi-Hamiltonian structure of Sutherland models coupled to two $\mathfrak{u}(n{)}^{\ast }$-valued spins from Poisson reduction
• Poisson-Nijenhuis structures on quiver path algebras