original larger C\*-algebra. We define the gauge transformations, explain how to enforce the Gauss law constraint, show that the dynamics automorphism group descends to the algebra of physical observables and prove that gauge invariant ground states exist.'
author:
- |
    [Hendrik Grundling]{}\
    [Department of Mathematics,]{}\
    [University of New South Wales,]{}\
    [Sydney, NSW 2052, Australia.]{}\
    [hendrik@maths.unsw.edu.au]{}\
    [FAX: +61-2-93857123]{}\
- |
    [Gerd Rudolph ]{}\
    [Institut für Theoretische Physik,]{}\
    [Universität Leipzig,]{}\
    [Postfach 100 920, D-4109 Leipzig.]{}\
    [rudolph@rz.uni-leipzig.de]{}\
    [FAX: +49-341-9732548]{}
title: '**Dynamics for QCD on an infinite lattice**'
---

Introduction
============

In a previous paper ([@GrRu]) we constructed in a C\*-algebraic context a suitable field algebra which can model the kinematics of Hamiltonian QCD on an infinite lattice in $\R^3$. It was based on the finite lattice model for Hamiltonian QCD developed by Kijowski, Rudolph (cf. [@KR; @KR1]). We did not consider dynamics, and the construction and analysis of the dynamics for QCD on an infinite lattice is the main problem which we want to address in this paper. For reasons to be explained, we will not here directly use the C\*-algebra which we constructed before for dynamics construction, but will follow a different approach.

Whilst the algebra constructed in [@GrRu] contained all the 