GLOBAL GAUSS LAW FOR LATTICE QCD

Abstract

In the present paper we analyze the gauge invariant content of the Gauss law and the notion of global charge in lattice quantum chromodynamics (QCD). For this purpose, we discuss the field algebra and the observable algebra of this theory in some detail. This contribution should be understood as a first step in the direction of investigating the nonperturbative structure of QCD, the final aim being an effective microscopic theory of interacting hadrons. We stress that standard methods from algebraic quantum field theory for models which do not contain massless particles, see , do not apply here. Some progress towards an implementation of similar ideas for theories with massless particles has been made, for the case of quantum electrodynamics (QED) see 3 and 4 and further references therein. For some attempts to deal with the nonabelian case we refer to papers by Strocchi and Wightman, see 5 and , and for the study of a Z2-gauge theory see . In QED, the notion of global (electric) charge is easy to understand. This is due to the fact, that in this theory we have a local Gauss law, which is built from gauge invariant operators and which is linear. Thus, one can “sum up” the local Gauss laws over all points of a given (spacelike) hyperplane in space time yielding the following gauge invariant conservation law: The global electric charge is equal to the electric flux through a 2-sphere at infinity. On the contrary, in QCD the local Gauss law is neither built from gauge invariant operators nor is it linear. The main point of the present paper is