  We study the ultraviolet problem for quantum electrodynamics on a three
dimensional torus. We start with the lattice gauge theory on a toroidal lattice
and seek to control the singularities as the lattice spacing is taken to zero.
This is done by following the flow of a sequence of renormalization group
transformations. The analysis is facilitated by splitting the space of gauge
fields into large and small fields at each step following Balaban. In this
paper we explore the first step in detail.
