Classical integrable systems and gauge field theories

2008/02/26 by M. A. Olshanetsky, M. Olshanetsky
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Black Holes and Theoretical Physics #Duality (order theory) #Euler's formula #Field (mathematics) #Gauge (firearms) #Gauge group #Gauge theory #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Symplectic geometry #Symplectomorphism #hep-th

paper · pdf · doi:10.1134/s1063779609010067

36 pages, Lectures given at Advanced Summer School on Integrable Systems and Quantum Symmetries (Prague, June, 2007)

arxiv created 2008/02/26 · openalex publication_date 2009/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this review we consider the Hitchin integrable systems and their relations with the self-duality equations and twisted super-symmetric Yang-Mills theory in four dimensions. We define the Symplectic Hecke correspondence between different integrable systems. As an example we consider the Elliptic Calogero-Moser system and integrable Euler-Arnold top on coadjoint orbits of the group GL (N, C) and explain the Symplectic Hecke correspondence for these systems.

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