  A variational method is discussed, based on the principle of minimal
variance. The method seems to be suited for gauge interacting fermions, and the
simple case of quantum electrodynamics is discussed in detail. The issue of
renormalization is addressed, and the renormalized propagators are shown to be
the solution of a set of finite integral equations. The method is proven to be
viable and, by a spectral representation, the multi-dimensional integral
equations are recast in one-dimensional equations for the spectral weights. The
UV divergences are subtracted exactly, yielding a set of coupled Volterra
integral equations that can be solved iteratively, and are known to have a
unique solution.
