The Dn Ruijsenaars-Schneider model
Kai Chen, Bo-yu Hou
TL;DR
This paper presents a Lax pair formulation for the Dn Ruijsenaars-Schneider integrable system, demonstrating its Liouville integrability and connection to the Calogero-Moser system through degenerations and limits.
Contribution
It provides the first explicit Lax pair for the Dn Ruijsenaars-Schneider model and establishes its integrability and relation to known systems.
Findings
Lax pair for Dn Ruijsenaars-Schneider model derived
Liouville integrability proven via involutive Hamiltonians
Degeneration to Calogero-Moser system shown
Abstract
The Lax pair of the Ruijsenaars-Schneider model with interaction potential of trigonometric type based on Dn Lie algebra is presented. We give a general form for the Lax pair and prove partial results for small n. Liouville integrability of the corresponding system follows a series of involutive Hamiltonians generated by the characteristic polynomial of the Lax matrix. The rational case appears as a natural degeneration and the nonrelativistic limit exactly leads to the well-known Calogero-Moser system associated with Dn Lie algebra.
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