Complete integrability of relativistic Calogero-Moser systems and elliptic function identities

@article{Ruijsenaars1987CompleteIO,
  title={Complete integrability of relativistic Calogero-Moser systems and elliptic function identities},
  author={Simon N. M. Ruijsenaars},
  journal={Communications in Mathematical Physics},
  year={1987},
  volume={110},
  pages={191-213}
}
  • S. Ruijsenaars
  • Published 1 June 1987
  • Mathematics
  • Communications in Mathematical Physics
Poincaré-invariant generalizations of the Galilei-invariant Calogero-MoserN-particle systems are studied. A quantization of the classical integralsS1, ...,SN is presented such that the operatorsŜ1, ...,ŜN mutually commute. As a corollary it follows thatS1, ...,SN Poisson commute. These results hinge on functional equations satisfied by the Weierstrass σ- and ℘-functions. A generalized Cauchy identity involving the σ-function leads to anN×N matrixL whose symmetric functions are proportional toS1… 
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