Hamiltonian Dynamics, Classical R-matrices and Isomonodromic Deformations

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

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

References in corpus (3)

• Quantum Inverse Scattering Method and Correlation Functions
• Fredholm Determinants, Differential Equations and Matrix Models
• Dual Isomonodromic Deformations and Moment Maps to Loop Algebras