  We discuss in detail potential NRQED (pNRQED), a previously proposed
effective field theory for ultrasoft photons. The pNRQED lagrangian for the
equal mass case is presented and it is shown that it correctly reproduces the
positronium spectrum at order $m\alpha^5$. The pNRQED lagrangian for the
unequal mass case is also presented at the same order. Dimensional
regularization is used throughout.

High Energy Physics - Phenomenology;Nuclear Theory;Atomic Physics