Hierarchy of Multipolar Terms For Non Relativistic Moving Atoms in QED

Abstract

In this article an hierarchy of terms in the expansion of the multipolar Hamiltonian for non relativistic moving atoms in QED is considered. The particular case of neutral composite systems of 2,3 and 4 particles is considered. The proposed hierarchy is based on a scaling analysis of the multipolar Hamiltonian together with a multipolar expansion of the coupling terms. We give explicit results up to the fourth order in the fine structure constant.