Hierarchy of Multipolar Terms For Non Relativistic Moving Atoms in QED

TL;DR

This paper develops a hierarchical framework for the multipolar Hamiltonian in non-relativistic QED, providing explicit results up to fourth order for neutral multi-particle systems, enhancing understanding of atomic interactions.

Contribution

It introduces a new hierarchy based on scaling analysis and multipolar expansion, offering explicit higher-order terms for non-relativistic moving atoms in QED.

Findings

Explicit multipolar Hamiltonian terms up to fourth order.

Hierarchy applicable to 2, 3, and 4 particle systems.

Enhanced precision in atomic interaction modeling.

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.