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

Jean Avan
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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 $N \rightarrow \infty$ limit realize the infinite Lie algebras Sdiff$({\Bbb R} \times S_1 )$ in the trigonometric case and Sdiff$({\Bbb R }^2)$ in the rational case. It is then isomorphic to the algebra of observables constructed in the two-dimensional collective string field theory.

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Jean Avan. 1994-01-12. Integrable extensions of the rational and trigonometric $A_N$ Calogero Moser potentials. https://doi.org/10.1016/0375-9601(94)90618-1

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