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.

In Section II the method of arXiv:1308.1836 is reviewed and used for QED