This article introduces one of the simplest examples of a quantum model with a gauge field, treating D-dimensional space as a lattice so that the math is straightforward. The model is a special case of compact quantum electrodynamics (compact QED), namely the case with no electrically charged matter, so the quantum electromagnetic field is the only physical entity.
The adjective compact in the name refers to the fact that the model uses the compact group U(1) as its gauged group, in contrast to traditional electrodynamics in which the gauged group is the noncompact group R. The choice U(1) is motivated by the fact that the electric charges of all known elementary particles appear to be precisely integer multiples of a single elementary unit of charge. The model constructed here does not include charged matter, but it uses U(1) as the gauged group to prepare for models that do.
