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 operators D(a) defined by some lattice gauge field a. We consider the Lagrangian D→tr((D(a)+im)^4) on D , where m Є C is a mass parameter. Critical points of this functional are given by solutions of a nonlinear discrete wave equation which describe the time evolution of the gauge fields a. In the simplest case, the dynamical system is a cubic Henon map. In general, it is a symplectic coupled map lattice. We prove the existence of non-trivial critical points in two examples.