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Abstract <p> We describe the Ruijsenaars action–angle duality in classical many-body integrable systems through the spectral duality transformation relating the classical spin chains and Gaudin models. For this purpose, the Lax matrices of many-body systems are represented in the multi-pole (Gaudin-like) form by introducing a fictitious spectral parameter. This form of Lax matrices is also interpreted as a classical–classical version of the quantum–classical duality. </p>

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Interrelations between dualities in classical integrable systems and a classical–classical version of the quantum–classical duality

  • 期刊论文

  • 发表日期：

    2025年2月25日

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  • R. A. Potapov,
  • A. V. Zotov

摘要

Abstract

We describe the Ruijsenaars action–angle duality in classical many-body integrable systems through the spectral duality transformation relating the classical spin chains and Gaudin models. For this purpose, the Lax matrices of many-body systems are represented in the multi-pole (Gaudin-like) form by introducing a fictitious spectral parameter. This form of Lax matrices is also interpreted as a classical–classical version of the quantum–classical duality.