Calogero model

Calogero models comprise several integrable systems in classical mechanics and their relatives; they are describing interacting systems of nn particles on a circle or on a line. Basic variants include Calogero-Moser system, Calogero-Sutherland system and “relativistic” Ruijsenaars model?s. Calogero-Moser system was a historical source of the study of Dunkl operators and Cherednik’s double Hecke algebras. The Calogero-Moser system can also be related to the rational nn-soliton solutions of rational KP equation; the elucidation of the relation between the soliton solutions and solutions of the Calogero-Moser system is rather deep and is called Calogero-Moser correspondence. Its modern formulation involves noncommutative algebraic geometry.

Some special functions come out of analysis of Calogero models, like Jack polynomials.

  • Pavel Etingof, Lectures on Calogero-Moser systems, pdf
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  • E. Mukhin, V. Tarasov, A. Varchenko, KZ characteristic variety as the zero set of classical Calogero-Moser Hamiltonians, arxiv/1201.3990
  • Sergio Andraus, Makoto Katori, Seiji Miyashita, Calogero-Moser systems as a diffusion-scaling transform of Dunkl processes on the line, arxiv/1211.6561

On Calogero-Moser correspondence:

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  • George Wilson, Collisions of Calogero-Moser particles and an adelic Grassmannian, With an appendix by I. G. Macdonald. Invent. Math. 133 (1998), no. 1, 1–41, MR99f:58107, doi
  • Yu. Berest, G. Wilson, Ideal classes of the Weyl algebra and noncommutative projective geometry (with an Appendix by M. Van den Bergh), Internat. Math. Res. Notices 26 (2002), 1347–1396.
  • Yu. Berest, G. Wilson, Mad subalgebras of rings of differential operators on curves, Advances in Math. 212 no. 1 (2007), 163–190.
  • V. Ginzburg, Non-commutative symplectic geometry, quiver varieties, and operads, Math. Res. Lett. 8 (2001), 377-400.
  • Yuri Berest, Oleg Chalykh, A A_\infty-modules and Calogero-Moser spaces, J. Reine Angew. Math. 607 (2007), 69–112, MR2009f:16019, doi

Last revised on November 29, 2012 at 20:24:39. See the history of this page for a list of all contributions to it.