Gauge invariance of quantum electrodynamics of multi-electron atoms

TL;DR

This paper addresses the challenge of proving gauge invariance in quantum electrodynamics for multi-electron atoms, proposing methods to establish invariance of atomic properties in complex systems.

Contribution

It introduces two approaches to prove gauge invariance for multi-electron atoms within an extended quantum electrodynamics framework.

Findings

Gauge invariance of atomic masses established in all perturbation orders.

Electromagnetic form factors of multi-electron atoms shown to be gauge invariant.

Methods applicable to complex nuclear interactions.

Abstract

The proof of gauge invariance of the quantum electrodynamics of photons and electrons does not apply directly to the quantum electrodynamics of photons, electrons, and nuclei because multi-electron atoms belong to the space of asymptotic states of the extended theory. We offer two possible ways to circumvent this problem and prove, using a fairly general model for the description of nucleon-nucleon interaction in nuclei, the gauge invariance of the masses and electromagnetic form factors of multi-electron atoms in all orders of perturbation theory.