Rayleigh-Sommerfeld diffraction integrals for relativistic wave equations

Here we apply the commonly used Rayleigh-Sommerfeld diffraction integral to the propagation of relativistic fields in spacetime, using the theory to find the propagators for both the Klein-Gordon equation and the Dirac equation. Based on these results, we find an interpretation of the Klein-Gordon equation in terms of the Feynman checkerboard model, as well as highlighting some apparently overlooked aspects of the Feynman checkerboard model as it is usually applied to the Dirac equation.