Multipolar quantum electrodynamics of localized charge-current distributions: Spectral theory and renormalization

TL;DR

This paper develops a spectral theory and renormalization approach for multipolar quantum electrodynamics involving localized charge-current distributions, generalizing the Lamb shift to complex atomic and molecular assemblies.

Contribution

It formulates a non-relativistic quantum field theory with a multipolar Hamiltonian derived via Power-Zienau-Woolley transformation, including perturbative renormalization for energy corrections.

Findings

Derived a renormalized energy shift generalizing the Lamb shift.

Provided a framework to analyze multipole contributions to energy levels.

Enabled study of quantum vacuum effects in complex atomic and molecular systems.

Abstract

We formulate a non-relativistic quantum field theory to model interactions between quantized electromagnetic fields and localized charge-current distributions. The electronic degrees of freedom are encoded in microscopic polarization and magnetization field operators whose moments are identified with the multipole moments of the charge-current distribution. The multipolar Hamiltonian is obtained from the minimal coupling Hamiltonian through a unitary transformation, often referred to as the Power-Zienau-Woolley transformation; we renormalize this Hamiltonian using perturbation theory, the result of which is used to compute the leading-order radiative corrections to the electronic energy levels due to interactions between the electrons and quantum vacuum fluctuations in the electromagnetic field. Our renormalized energy shift constitutes a generalization of the Lamb shift in atomic hydrogen, valid for general localized assemblies of atoms and molecules, possibly with net charge but absent free current. By expanding the fields in a series of multipole moments, our results can be used to study contributions to this energy shift coming from specific multipole moments of arbitrary order.