The Kapitza-Dirac effect is similar to the canonical experiment on diffraction of electrons through slits in an opaque screen, except that the diffraction grating has been replaced by a standing wave of light. Remarkably, incident electrons are diffracted by the standing light wave almost as if by a standard diffraction grating. Only recently has this effect been confirmed experimentally in this form [1], although it was originally predicted by Kapitza and Dirac almost 70 years ago. This paper examines the relativistic effects involved in this phenomena using the formalism of quantum field theory.