Ultraviolet regularity for QED in d=3

Abstract

We study the ultraviolet problem for QED 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 unit scale. This is accomplished by a nonpertubative technique which is insensitive to whether the renormalizations are finite or infinite.