On colliding ultrarelativistic nuclei on a transverse lattice

We argue that the classical evolution of small x modes in the collision of two ultrarelativistic nuclei is described on a transverse lattice by the Kogut--Susskind Hamiltonian in 2+1-dimensions coupled to an adjoint scalar field. The initial conditions for the evolution are provided by the non--Abelian Weizs\"acker--Williams fields which constitute the classical parton distributions in each of the nuclei. We outline how lattice techniques developed for real time simulations of field theories in thermal equilibrium can be used to study non--perturbatively, thermalization and classical gluon radiation in ultrarelativistic nuclear collisions.