This article constructs some of the simplest quantum models that are believed to have nontrivial continuum limits with Lorentz symmetry, even though they are initially defined by treating spacetime as a lattice. The only field used in the construction is a gauge field. When the gauged group is nonabelian, these are called Yang-Mills theories. The models are constructed using the path integral formulation, paying special attention to how Wick rotation is used to ensure that time evolution is unitary without compromising the intuitive reason to expect that the continuum limit has Lorentz symmetry. The relationship between the path integral and hamiltonian formulations is reviewed, including an explanation of how they handle observables that are extended in time.
