Integrable many-body systems of Calogero-Ruijsenaars type
arXiv:1705.01333 · doi:10.14232/phd.3595
Abstract
This thesis presents our results on Liouville integrable systems of Calogero-Ruijsenaars type: 1. We prove an explicit formula providing canonical spectral coordinates for the rational Calogero-Moser system. 2. We explore action-angle duality for the trigonometric BC(n) Sutherland system using Hamiltonian reduction. 3. We derive a Poisson-Lie deformation of the trigonometric BC(n) Sutherland system using Hamiltonian reduction. 4. We construct a Lax pair for the hyperbolic Ruijsenaars-Schneider system with two couplings. 5. We present an explicit construction of compactified trigonometric and elliptic Ruijsenaars-Schneider systems.
PhD thesis based on the author's papers arXiv:1407.2057, arXiv:1410.0301, arXiv:1503.01303, arXiv:1508.04991, arXiv:1601.01181, arXiv:1603.02877, arXiv:1603.06710, arXiv:1605.09736 . 218 pages, 8 figures
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