On third Poisson structure of KdV equation

Abstract

The third Poisson structure of KdV equation in terms of canonical ``free fields'' and reduced WZNW model is discussed. We prove that it is ``diagonalized'' in the Lagrange variables which were used before in formulation of 2D gravity. We propose a quantum path integral for KdV equation based on this representation.Comment: 6pp, Latex. to appear in ``Proceedings of V conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta, June 1994'' Teor.Mat.Fiz. 199