The theory of electromagnetic (EM) phenomena known as electrodynamics is one of the major theories in science. At macroscopic scales the interaction of the EM field with matter is described by the classical electrodynamics based on the Maxwell-Lorentz theory. Many of electromagnetic phenomena at microscopic scales are covered by the so-called semiclassical theory that treats the matter according to the quantum mechanics, whereas the EM field is treated classically. The subject of this presentation is a recently advanced by us neoclassical electromagnetic theory that describes EM phenomena at all spatial scales –microscopic and macroscopic. This theory modifies the classical electrodynamics into a theory that applies to all spatial scales including atomic and nanoscales. The neoclassical theory is conceived as one theory for all spatial scales in which the classical and quantum aspects are naturally unified and emerge as approximations. It is a classical Lagrangian field theory, and consequently it is a local and deterministic theory. Probabilistic aspects of the theory may arise in it effectively through complex nonlinear dynamical evolution. This presentation is to provide an introduction to our theory including a concise historical review.

(Joint work with Anatoli Babin)