Foldy-Wouthuysen transformation of quantum electrodynamics and relativistic corrections to the transition operator in two-electron systems

Abstract

A Foldy-Wouthuysen transformation is obtained for use in the field theory of quantum electrodynamics. The gauge invariance of quantum electrodynamics and the fact that the transformation function depends on time only through the photon field are essential for the success of this transformation. Transition operators which include leading relativistic corrections beyond $\overrightarrow{\mathrm{p}}·\overrightarrow{\mathrm{A}}$ are obtained. It is shown that the ${\overrightarrow{\mathrm{A}}}^2$ term in the interaction Hamiltonian contributes. Applications are made to the spin-forbidden and spin-allowed transitions in heliumlike systems.