On Calculation of Amplitudes in Quantum Electrodynamics
  A new method of calculation of amplitudes of different processes in quantum electrodynamics is proposed. The method does not use the Feynman technique of trace of product of matrices calculation. The method strongly simplifies calculation of cross sections for different processes. The effectiveness of the method is shown on the cross-section calculation of Coulomb scattering, Compton scattering and electron-positron annihilation. 
Kostyantyn Karplyuk and Oleksandr Zhmudsky
hep-ph hep-th quant-ph