The NRQED Hamiltonian and photon-exchange interaction up to mα8 order
Abstract
We derive the effective Hamiltonian of the Nonrelativistic Quantum Electrodynamic up to mα8 by using scattering matching approach. At mα6 order, these results are coincide with Pachucki's, which is obtained by applying Foldy-Wouthuysen transformation. And by using the NRQED Hamiltonian, we derive the photon-exchange interaction in non-retarded approximation and the retardation correction up to mα8. The energy shift of the photon-exchange interaction is obtained by studying the pole of the total Green function.
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