Babin A., Figotin A. Neoclassical Theory of Electromagnetic Interactions. A Single Theory for Macroscopic and Microscopic Scales

Springer-Verlag London, 2016 — 696p. — (Theoretical and Mathematical Physics) — ISBN: 978-1-4471-7284-0 (eBook), 978-1-4471-7282-6 (Hardcover).In this monograph, the authors present their recently developed theory of electromagnetic interactions. This neoclassical approach extends the classical electromagnetic theory down to atomic scales and allows the explanation of various non-classical phenomena in the same framework.
While the classical Maxwell–Lorentz electromagnetism theory succeeds in describing the physical reality at macroscopic scales, it struggles at atomic scales. Here, quantum mechanics traditionally takes over to describe non-classical phenomena such as the hydrogen spectrum and de Broglie waves. By means of modifying the classical theory, the approach presented here is able to consistently explain quantum-mechanical effects, and while similar to quantum mechanics in some respects, this neoclassical theory also differs markedly from it. In particular, the newly developed framework omits probabilistic interpretations of the wave function and features a new fundamental spatial scale which, at the size of the free electron, is much larger than the classical electron radius and is relevant to plasmonics and emission physics.
This book will appeal to researchers interested in advanced aspects of electromagnetic theory. Treating the classical approach in detail, including non-relativistic aspects and the Lagrangian framework, and comparing the neoclassical theory with quantum mechanics and the de Broglie–Bohm theory, this work is completely self-contained.The History of Views on Charges, Currents and the Electromagnetic Field
The Neoclassical Field Theory of Charged Matter: A Concise Presentation
The Maxwell Equations
Dipole Approximation for Localized Distributed Charges
The Minkowski Four-Dimensional Spacetime and Relativistic Kinematics
Longitudinal and Transversal Fields
Non-relativistic Quasistatic Approximations
Electromagnetic Field Lagrangians
Variational Principles, Lagrangians, Field Equations and Conservation Laws
Lagrangian Field Formalism for Charges Interacting with EM Fields
Lagrangian Field Formalism for Balanced Charges
Lagrangian Field Formalism for Dressed Charges
Rest and Time-Harmonic States of a Charge
Uniform Motion of a Charge
Accelerating Wave-Corpuscles
Interaction Theory of Balanced Charges
Relation to Quantum Mechanical Models and Phenomena
The Theory of Electromagnetic Interaction of Dressed Charges
Comparison of EM Aspects of Dressed and Balanced Charges TheoriesThe Dirac Equation
Basics of Spacetime Algebra (STA)
The Dirac Equation in the STA
The Basics of the Neoclassical Theory of Charges with Spin 1/2
Neoclassical Free Charge with Spin
Neoclassical Solutions: Interpretation and Comparison with the Dirac Theory
Clifford and Spacetime Algebras
Multivector Calculus
Relativistic Concepts in the STA
Electromagnetic Theory in the STA
The Wave Function and Local Observables in the STA
Multivector Field Theory
Trajectories of Concentration
Energy Functionals and Nonlinear Eigenvalue Problems
Elementary Momentum Equation Derivation for NKG
Fourier Transforms and Green Functions
Splitting of a Field into Gradient and Sphere-Tangent Parts
Hamilton–Jacobi Theory
Point Charges in a Spatially Homogeneous Electric Field
Statistical and Wave Viewpoints in Hamilton–Jacobi Theory
Almost Periodic Functions and Their Time-Averages
Vector Formulas
The Helmholtz Decomposition
Gaussian Wave Packets