About Local-Field Theory Based on Electron–Photon Wave Mechanics

Abstract

It appears from the description in various chapters of Part I that the local-field concept plays a central role in near-field and mesoscopic electrodynamics. Since the local fields vary considerably on the atomic length scale studies of the particle dynamics cannot be based on the Newton–Lorentz equation, as it was done originally by Lorentz [138, 172] in his ambitious program of “separating matter and aether” [18, 27, 173]. By replacing Newtonian mechanics by its nonclassical covering theory, i.e., nonrelativistic wave mechanics, one obtains a satisfactory starting point for most theoretical studies in near-field and mesoscopic electrodynamics. Many aspects of local-field electrodynamics are covered in the reviews by Cho [174], Stahl and Balslev [175], and the present author [5, 49]. In a few cases it may be necessary also to replace Newtonian mechanics by its classical covering, viz., relativistic mechanics. This will be the case, for instance, when a relativistic particle moves parallel to a surface in the evanescent tail of a surface wave or penetrates a condensed-matter medium. Relativistic aspects of local-field electrodynamics can be of importance in microscopic response theory.Thus, when an object under study moves with respect to the source exciting the object (or/and the detector receiving the object response) it may be necessary to make an inertial-frame independent calculation of the microscopic response function of the object, even if the relative velocity of object and source (detector) is small. The relativistic wave mechanics of massive particles (electrons) is of interest in near-field studies where the electron spin dynamics plays a role. Although it in most cases is sufficient to base the practical calculations on the weakly-relativistic Pauli equation, it might be necessary for a fundamental understanding to start from the fully-relativistic Dirac equation. The spatial localization problem for photons cannot, at least from my standpoint, be fully explored without involving the field–matter interaction. In fact, I have argued on several occasions that it is the Compton wavelength of the electron which sets the fundamental limit for how strongly localized a photon can be prepared in space; see e.g., [176].