One-parameter discrete-time Calogero–Moser system

U. Jairuk^a, S. Yoo-Kong<sup>b

a</sup> Division of Physics, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Pathumthani, Thailand
^b The Institute for Fundamental Study, Naresuan University, Phitsanulok, Thailand

Abstract: We present a new type of integrable one-dimensional many-body systems called a one-parameter Calogero–Moser system. At the discrete level, the Lax pairs with a parameter are introduced and the discrete-time equations of motion are obtained as together with the corresponding discrete-time Lagrangian. The integrability property of this new system can be expressed in terms of the discrete Lagrangian closure relation by using a connection with the temporal Lax matrices of the discrete-time Ruijsenaars–Schneider system, an exact solution, and the existence of a classical $r$-matrix. As the parameter tends to zero, the standard Calogero–Moser system is recovered in both discrete-time and continuous-time forms.

Keywords: one-parameter, discrete-time Calogero–Moser system, discrete-time Ruijsenaars–Schneider system, closure relation.

MSC: 70

Received: 10.06.2023
Revised: 02.08.2023

DOI: 10.4213/tmf10569

 English version: Theoretical and Mathematical Physics, 2024, 218:3, 357–369

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