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 (γ⋅Π)2, with Πμ=pμ−eAμ. In this basis, the transformation
acquires a free form involving the dynamical quantum numbers induced by the
field.Comment: 8 pages. Accepted in J. Phys. A: Math. and Theo. (Fast Track
Communication