RG flows on the phase spaces and the $τ$ functions for the generic Hamiltonian systems

Details RG flows on the phase spaces and the $τ$ functions for the generic Hamiltonian systems RG flows on the phase spaces and the $τ$ functions for the generic Hamiltonian systems

2000-10-10

arxiv.org/abs/hep-th/0010068v3

Phys.Lett. B498 (2001) 211-217; Erratum-ibid. B504 (2001) 362

Physics

High Energy Physics

High Energy Physics - Theory

typos corrected, published in Phys. Lett. B

Scientific paper

10.1016/S0370-2693(01)00003-X

We discuss the generic definition of the $\tau$ 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 $\tau$ 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.

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