Derivation of the Lamb shift using an effective field theory

We rederive the O(a^5) shift of the hydrogen levels in the nonrecoil limit (me/mp -> 0) using an extension of nonrelativistic QED (NRQED), an effective field theory developed by Caswell and Lepage. Our result contains the Lamb shift as a special case. Although this calculation is not new, it is presented here for the first time using the modem language of effective field theories. It clearly illustrates the usefulness of applying a multipole expansion to the NRQED vertices.