Interrelations between dualities in classical integrable systems and classical-classical version of quantum-classical duality
arXiv:2410.19035 · doi:10.1134/S0040577925020059
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 classical-classical version of quantum-classical duality.
24 pages, reference added
References in corpus (17)
- Darboux coordinates, Yang-Yang functional, and gauge theory
- Ding-Iohara-Miki symmetry of network matrix models
- Explicit examples of DIM constraints for network matrix models
- On Double-Elliptic Integrable Systems. 1. A Duality Argument for the case of SU(2)
- Spectral Duality Between Heisenberg Chain and Gaudin Model
- Spectral Duality in Integrable Systems from AGT Conjecture
- Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems
- Self-duality of the compactified Ruijsenaars-Schneider system from quasi-Hamiltonian reduction
- Spectral dualities in XXZ spin chains and five dimensional gauge theories
- KZ Characteristic Variety as the Zero Set of Classical Calogero-Moser Hamiltonians
- Trigonometric version of quantum-classical duality in integrable systems
- Three-particle Integrable Systems with Elliptic Dependence on Momenta and Theta Function Identities
- Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles
- Supersymmetric quantum spin chains and classical integrable systems
- Dualities in quantum integrable many-body systems and integrable probabilities -- I
- KZ-Calogero correspondence revisited
- Nested Bethe Ansatz and Finite Dimensional Canonical Commutation Relations