Red light, blue light, Feynman and a layer of glass: the causal propagator

A propagator–description approach of the propagation of EM waves is provided, in complex situations with underlying boundary conditions. To this end, the so-called Schwinger–Feynman causal propagator is explicitly derived, and spelled out, for the first time, for transmission of a photon through, and reflection off, a layer of glass of flat parallel surfaces. In a very general context, the corresponding transition amplitudes of a polarized or unpolarized photon are obtained, and the conservation of probabilities, and the underlying consistency conditions of the results, are established. Inspired by Feynman’s intuitive and well-publicized non-technical treatment of such a problem with red and blue light, one, in a quantum view-point, is interested in the probabilities of the events just described in determining the fate of a photon. This analysis provides an alternative way of looking at the problem in question, through propagation of photons, as a physically more appealing approach, in Feynman’s spirit, than by matching plane waves at boundaries as we often do. It also shows how a propagator may be derived, in more complex situations with specific boundary conditions, than just simply in infinite extended spaces. Finally, it is hoped that this work will be stimulating and of interest to practitioners with different emphases on EM wave propagation.