The NRQED Hamiltonian and photon-exchange interaction up to $m\alpha^8$ order

TL;DR

This paper derives an effective NRQED Hamiltonian up to order $m\alpha^8$, providing detailed photon-exchange interactions and corrections, advancing precision in quantum electrodynamics calculations.

Contribution

It introduces a new derivation of the NRQED Hamiltonian up to $m\alpha^8$ order using scattering matching, aligning with previous results at lower orders and extending to higher-order photon interactions.

Findings

Derived the NRQED Hamiltonian up to $m\alpha^8$ order.

Calculated photon-exchange interactions including retardation effects.

Provided energy shift calculations via Green function analysis.

Abstract

We derive the effective Hamiltonian of the Nonrelativistic Quantum Electrodynamic up to $m\alpha^8$ by using scattering matching approach. At $m\alpha^6$ 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 $m\alpha^8$. The energy shift of the photon-exchange interaction is obtained by studying the pole of the total Green function.