Renormalization group on the phase and the gamma functions for the generic Hamiltonian systems

Abstract

We discuss the generic definition of the τ function for the arbitrary Hamiltonian system. The different approaches concerning the deformations of the curves and surfaces are compared. It is shown that the Baker–Akhiezer function for the secondary integrable system of the Toda lattice type can be identified with the coherent wave function of the initial dynamical system. The τ function appears to be related to the filling of the interior of the classical trajectory by coherent states. Transition from dispersionless to dispersionful Toda lattice corresponds to the quantization of the initial dynamical system.