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

## TL;DR

This paper develops a discrete phase space approach to relativistic quantum electrodynamics, deriving Feynman diagrams and S-matrix elements, and presents a divergence-free Coulomb potential approximation for electron-electron scattering.

## Contribution

It introduces a discrete phase space formulation for relativistic QED, providing explicit calculations and a non-singular Coulomb potential approximation.

## Key findings

- Derived Feynman diagrams and S-matrix elements in discrete phase space.
- Obtained a divergence-free Coulomb potential approximation.
- Explicit second order S-matrix element for Moller scattering.

## Abstract

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.