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

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

1993-06-22

arxiv.org/abs/hep-th/9306112v3

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/0375-9601(94)90618-1

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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