Gauge invariance and relativistic effects in photon absorption and scattering by matter

TL;DR

This paper addresses the gauge invariance problem in photon absorption and scattering calculations, proposing a fully relativistic approach via quantum electrodynamics and a new many-body transformation to improve semi-relativistic methods.

Contribution

It introduces a fully relativistic framework for photon interactions and a novel Foldy-Wouthuysen transformation to accurately include relativistic effects.

Findings

Relativistic cross-sections are obtained using quantum electrodynamics.

The new transformation simplifies relativistic correction calculations.

A significant spin-position interaction affects magnetic x-ray circular dichroism.

Abstract

There is an incompatibility between gauge invariance and the semi-classical time-dependent perturbation theory commonly used to calculate light absorption and scattering cross-sections. There is an additional incompatibility between perturbationtheory and the description of the electron dynamics by a semi-relativistic Hamiltonian.In this paper, the gauge-dependence problem of exact perturbation theory is described, the proposed solutions are reviewed and it is concluded that none of them seems fully satisfactory. The problem is finally solved by using the fully relativistic absorption and scattering cross-sections given by quantum electrodynamics. Then, a new many-body Foldy-Wouthuysen transformation is presented to obtain correct semi-relativistic transition operators.This transformation considerably simplifies the calculation of relativistic corrections. In the process, a new light-matter interaction term emerges, called the spin-position interaction, that contributes significantly to the magnetic x-ray circular dichroism of transition metals.We compare our result with the ones obtained by using several semi-relativistic time-dependent Hamiltonians. In the case of absorption, the final formula agrees with the result obtained from one of them. However, the correct scattering cross-section is not given by any of the semi-relativistic Hamiltonians.