Free form of the Foldy-Wouthuysen transformation in external electromagnetic fields

Abstract

We derive the exact Foldy-Wouthuysen transformation for Dirac fermions in a time-independent external electromagnetic field in the basis of the Ritus eigenfunctions, namely the eigenfunctions of the operator (gamma . Pi)(2), with Pi(mu) = p(mu) - eA(mu). On this basis, the transformation acquires a free form involving the dynamical quantum numbers induced by the field.