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experiment on diffraction of electrons through slits in an opaque screen, except that the diffraction grating has been replaced by a standing wave of light.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, 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.