 The perturbation part of the Hamiltonian comes out to be

In this treatment, the electron's spin coupling to the EM field is neglected.The scalar potential formula_32 set to zero either by imposing the Weyl gauge formula_33 or by working in the Coulomb gauge formula_34 in which formula_32 becomes negligibly small far from the sources.Either way, the commutator formula_36 is taken to be zero.