# 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} }

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…

## 441 Citations

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- Physics
- 1999

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- 2006

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- 1999

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- 1993

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- 2001

We consider the classical elliptic Calogero-Moser model. A set of canonical separated variables for this model has been constructed in Kuznetsov et al. However, the generating function of the…

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- 2014

A bstractAn old conjecture claims that commuting Hamiltonians of the double-elliptic integrable system are constructed from the theta-functions associated with Riemann surfaces from the…

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- Mathematics
- 2004

The deformed quantum Calogero-Moser-Sutherland problems related to the root systems of the contragredient Lie superalgebras are introduced. The construction is based on the notion of the generalized…

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- Mathematics
- 2009

In this series of papers we study Hilbert-Schmidt integral operators acting on the Hilbert spaces associated with elliptic Calogero-Moser type Hamiltonians. As shown in this first part, the integral…

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