Discrete Phase Space, Relativistic Quantum Electrodynamics, and a Non-Singular Coulomb Potential

This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent relativistic quantum electrodynamics, the corresponding Feynman diagrams and S#-matrix elements are derived. In the special case of electron-electron scattering (Moller scattering), the explicit second order element <f|S#(2)|i> is deduced. Moreover, assuming the slow motions for two external electrons, the approximation of <f|S#(2)|i> yields a divergence-free Coulomb potential.