Abstract
Poincaré-invariant generalizations of the Galilei-invariant Calogero-MoserN-particle systems are studied. A quantization of the classical integralsS 1, ...,S N is presented such that the operatorsŜ 1, ...,Ŝ N mutually commute. As a corollary it follows thatS 1, ...,S N 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 toS 1, ...,S N .
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Communicated by A. Jaffe
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Ruijsenaars, S.N.M. Complete integrability of relativistic Calogero-Moser systems and elliptic function identities. Commun.Math. Phys. 110, 191–213 (1987). https://doi.org/10.1007/BF01207363
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DOI: https://doi.org/10.1007/BF01207363