  Relativistic Hamiltonians, derived from the path integrals, are known to
provide a simple and useful formalism for hadrons spectroscopy in QCD. The
accuracy of this approach is tested using the QED systems, and the calculated
spectrum is shown to reproduce exactly that of the Dirac hydrogen atom, while
the Breit-Fermi nonrelativistic expansion is obtained using Foldy-Wouthuizen
transformation. Calculated positronium spectrum, including spin-dependent
terms, coincides with the standard QED perturbation theory to the considered
order O(alpha^s).
