On the photon–classical electromagnetic field relationship

This paper discusses how the two ways in which the wavefunction of a free-propagating photon can be introduced—starting from the relativistic energy−momentum relationship or based on the electromagnetic field, in particular on Riemann–Silberstein vectors—are not entirely equivalent since they can lead to different consequences regarding photon localization. In the first case, a phase space localization in regions of the order of Planck's constant, in agreement with the quantum uncertainty principle, could be unambiguously obtained. In the second case, the choice of canonically conjugate variables and Fourier transforms determines if the state is treated quantumly or classically. Both formalisms are, however, compatible.