Ultraviolet regularity for QED in d = 3

We study the ultraviolet problem for quantum electrodynamics in d = 3 using Balaban’s formulation of the renormalization group. The model is defined on a fine toroidal lattice and we seek control as the lattice spacing goes to zero. As a first step, we take a bounded field approximation and solve the renormalization problem. Namely, we show that the bare energy density and the bare fermion mass can be chosen to depend on the lattice spacing, so that under the renormalization group flow they take preassigned values on a macroscopic scale. This is accomplished by a nonperturbative technique which is insensitive to whether the renormalizations are finite or infinite.