Calculating propagators for relativistic wave equations

Here we examine the propagation of relativistic fields in space-time using the viewpoint applied to derive the Rayleigh–Sommerfeld diffraction integral in three-dimensional space. We use this theory to find the propagators for both the Klein–Gordon equation and the Dirac equation. Based on these results, we highlight some apparently overlooked aspects of the Feynman checkerboard model as it is usually applied to the Dirac equation.