Hamiltonian Dynamics, Classical R-matrices and Isomonodromic Deformations
solv-int
2009-10-30 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
The Hamiltonian approach to the theory of dual isomonodromic deformations is developed within the framework of rational classical R-matrix structures on loop algebras. Particular solutions to the isomonodromic deformation equations appearing in the computation of correlation functions in integrable quantum field theory models are constructed through the Riemann-Hilbert problem method. The corresponding -functions are shown to be given by the Fredholm determinant of a special class of integral operators.
Cite
@article{arxiv.solv-int/9710012,
title = {Hamiltonian Dynamics, Classical R-matrices and Isomonodromic Deformations},
author = {J. Harnad},
journal= {arXiv preprint arXiv:solv-int/9710012},
year = {2009}
}
Comments
LaTeX 13pgs (requires lamuphys.sty). Text of talk given at workshop: Supersymmetric and Integrable Systems, University of Illinois, Chicago Circle, June 12-14, 1997. To appear in: Springer Lecture notes in Physics