Topological Charge in Lattice Gauce Theory

Lattice regularization has proved to be succesful in the numerical solution of asymptotically free quantum field theories [1, 2]. However it is believed that lattice regularization changes the semicalssical structure of the theories considerably. The reason is that states of the continuum theory with different topological charge are connected by singular gauge transformations [3]. With finite lattice spacing there are no singularities. Consequently one expects no tunneling in lattice theories. The aim of the present study is to show the existence of topological structure in lattice gauge theory. I give a simple expression for the topological charge of lattice gauge theories in four dimensions and I present the preliminary result of a Monte Carlo calculation of the distribution of this quantity on a small lattice In SU(2) gauge theory. The measured distribution is compatible with the dilute gas picture of certain pseudoparticles.