NONLINEAR DYNAMICS FROM THE WILSON LAGRANGIAN

A nonlinear Hamiltonian dynamics is derived from the Wilson action in lattice gauge theory. Let D be a linear space of lattice Dirac operato rs D(a) defined by some lattice gauge held a. We consider the Lagrangi an D bar arrow pointing right tr((D(a) + im)(4)) on D, where m is an e lement of C is a mass parameter. Critical points of this functional ar e given by solutions of a nonlinear discrete wave equation which descr ibe the time evolution of the gauge fields a. In the simplest case, th e dynamical system is a cubic Henon map. In general, it is a symplecti c coupled map lattice. We prove the existence of non-trivial critical points in two examples.