Dynamics of an almost lattice gauge theory realized by an ultracold atom system

Recently carried out experiments with ultracold atoms have realized the first building blocks to simulate lattice gauge theories quantum. Despite the great progress, the influence of experimental imperfections on the phase structure or the non-equilibrium dynamics is unclear. In this thesis we study the effect of terms violating the local gauge invariance as they occur in a typical experimental setup. In particular, we focus on ultracold atom setups which exploit angular momentum conservation in order to realize local gauge invariance. We also study the influence of dissipation in these systems and compare the dynamics of a theory with exact and almost lattice gauge theory. Especially we determine the time scales and observables when the difference between the two theories becomes significant.