Hamiltonian Dynamics, Classical R-matrices and Isomonodromic Deformations

Details Hamiltonian Dynamics, Classical R-matrices and Isomonodromic Deformations Hamiltonian Dynamics, Classical R-matrices and Isomonodromic Deformations

1997-10-18

arxiv.org/abs/solv-int/9710012v1

Lect.Notes Phys.502:63-75,1998

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX 13pgs (requires lamuphys.sty). Text of talk given at workshop: Supersymmetric and Integrable Systems, University of Illi

Scientific paper

10.1007/BFb0105314

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 $\tau$-functions are shown to be given by the Fredholm determinant of a special class of integral operators.

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