Communications in Mathematical Physics

, Volume 359, Issue 1, pp 1–60 | Cite as

Self-Duality and Scattering Map for the Hyperbolic van Diejen Systems with Two Coupling Parameters (with an Appendix by S. Ruijsenaars)

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Abstract

In this paper, we construct global action-angle variables for a certain two-parameter family of hyperbolic van Diejen systems. Following Ruijsenaars’ ideas on the translation invariant models, the proposed action-angle variables come from a thorough analysis of the commutation relation obeyed by the Lax matrix, whereas the proof of their canonicity is based on the study of the scattering theory. As a consequence, we show that the van Diejen system of our interest is self-dual with a factorized scattering map. Also, in an appendix by S. Ruijsenaars, a novel proof of the spectral asymptotics of certain exponential type matrix flows is presented. This result is of crucial importance in our scattering-theoretical analysis.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Bolyai InstituteUniversity of SzegedSzegedHungary
  2. 2.MTA Lendület Holographic QFT Group, Wigner RCPBudapest 114Hungary

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