QED spectra in the path integral formalism

Relativistic Hamiltonians, derived from the path integrals, are known to provide a simple and useful formalism for hadron 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. The calculated positronium spectrum, including spin-dependent terms, coincides with the standard QED perturbation theory to the considered order $O({\alpha }^4)$.