On the superintegrability of the rational Ruijsenaars-Schneider model
V. Ayadi, L. Feher
TL;DR
This paper proves the superintegrability of the rational Ruijsenaars-Schneider model by explicitly constructing additional conserved quantities, extending known methods from related integrable systems.
Contribution
It provides an alternative proof of superintegrability for the rational Ruijsenaars-Schneider model using a generalized Wojciechowski construction.
Findings
The rational Ruijsenaars-Schneider model is maximally superintegrable.
Explicit conserved quantities are constructed for the model.
The approach generalizes previous methods from the rational Calogero model.
Abstract
The rational and hyperbolic Ruijsenaars-Schneider models and their non-relativistic limits are maximally superintegrable since they admit action variables with globally well-defined canonical conjugates. In the case of the rational Ruijsenaars-Schneider model we present an alternative proof of the superintegrability by explicitly exhibiting extra conserved quantities relying on a generalization of the construction of Wojciechowski for the rational Calogero model.
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