On double-elliptic integrable systems

1999/06/29 by H. W. Braden, A. Marshakov, А. Миронов +3 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Angular momentum #Black Holes and Theoretical Physics #Classical mechanics #Coordinate system #Duality (order theory) #Elliptic coordinate system #Elliptic function #Geometry #Integrable system #Limiting #Mathematical analysis #Mathematical physics #Mathematics #Momentum (technical analysis) #Nonlinear Waves and Solitons #Physics #Pure mathematics #Spherical coordinate system #Torus #hep-th

paper · pdf · doi:10.1016/s0550-3213(99)00739-7

15 pages, LaTeX

arxiv created 1999/06/29 · openalex publication_date 2000/05/01 · arxiv updated 2009/11/30 · openalex created_date 2022/10/07 · openalex updated_date 2026/04/04

Abstract

We construct a two parameter family of 2-particle Hamiltonians closed under the duality operation of interchanging the (relative) momentum and coordinate. Both coordinate and momentum dependence are elliptic, and the modulus of the momentum torus is a non-trivial function of the coordinate. This model contains as limiting cases the standard Ruijsenaars-Calogero and Toda family of Hamiltonians, which are at most elliptic in the coordinates, but not in the momenta.

Citations

• Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
• D-branes, monopoles and Nahm equations
• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
• Insights and puzzles from branes: 4d SUSY Yang-Mills from 6d models
• Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD
• PREPOTENTIALS OF N=2 SUPERSYMMETRIC GAUGE THEORIES AND SOLITON EQUATIONS

Cited by

• TOWARDS A PROOF OF AGT CONJECTURE BY METHODS OF MATRIX MODELS
• The Atiyah–Hitchin bracket and the open Toda lattice
• Basic Properties of Non-Stationary Ruijsenaars Functions