Photon Wave Mechanics: Energy Wave Function and Four-Potential Theories
On the basis of the electromagnetic field vectors a photon wave function can be constructed in various manners. From a physical point of view different choices are in a sense equivalent provided they satisfy the free-space Maxwell equations. In order to make the quantum mechanical description of all, massive and non-massive, particles uniform certain choices are more attractive than others, however. In the complex field theory discussed in Chap. 15, the vectorial wave functions for the two photon helicity states are related to the electromagnetic field in a manner which is spatially nonlocal but timely local. This asymmetry between the space and time connections makes the complex field theory less attractive from a relativistic point of view. It appears from the analysis in Sect. 15.7 that the nonlocality in the spatial connection between field and wave function originates in the fact that the normalization constant Nβ(q) depends on the photon wave number. In this chapter we shall study two choices for a photon wave function which both connect the wave function and the electromagnetic field locally in space and time. From a relativistic point of view both choices are quite satisfactory.