dynamics on a concrete C\*-algebra which is “maximally large” in the sense that it contains all the true local kinematics C\*-algebras, and it is contained in the multiplier algebra of our previous kinematics field algebra. We will then take our new kinematics field C\*-algebra to be the smallest subalgebra which contains all the true local kinematics C\*-algebras, and is preserved w.r.t. the dynamics. Thus, the dynamics itself, will create the kinematics algebra for the system. The methods we use for the proof come from the application and generalization of Lieb–Robinson bounds on lattice systems (cf. [@NaSi; @NaSi2]). Moreover, we will see that the dynamics is strongly continuous on our new kinematics algebra.

On the algebra we construct here, we are able to define both the dynamics and the gauge transformations of our model. We will prove that the dynamics automorphism group commutes with the action of the group of local gauge transformations, hence the dynamics automorphism group action descends to the algebra of physical observables. We will prove the existence of gauge invariant ground states, which therefore produces ground states on the algebra of physical observables.

The cost of using this new algebra, is that it contains infinitely many nonphysical 