Neoclassical Theory of Electromagnetic Interactions: A Single Theory for Macroscopic and Microscopic Scales (Theoretical and Mathematical Physics)

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. Front Matter....Pages i-xxiii Introduction....Pages 1-6 The History of Views on Charges, Currents and the Electromagnetic Field....Pages 7-48 The Neoclassical Field Theory of Charged Matter: A Concise Presentation....Pages 49-85 Front Matter....Pages 87-87 The Maxwell Equations....Pages 89-100 Dipole Approximation for Localized Distributed Charges....Pages 101-105 The Minkowski Four-Dimensional Spacetime and Relativistic Kinematics....Pages 107-118 Longitudinal and Transversal Fields....Pages 119-126 Non-relativistic Quasistatic Approximations....Pages 127-139 Electromagnetic Field Lagrangians....Pages 141-151 Front Matter....Pages 153-154 Variational Principles, Lagrangians, Field Equations and Conservation Laws....Pages 155-179 Lagrangian Field Formalism for Charges Interacting with EM Fields....Pages 181-217 Lagrangian Field Formalism for Balanced Charges....Pages 219-228 Lagrangian Field Formalism for Dressed Charges....Pages 229-235 Front Matter....Pages 237-238 Rest and Time-Harmonic States of a Charge....Pages 239-277 Uniform Motion of a Charge....Pages 279-289 Accelerating Wave-Corpuscles....Pages 291-322 Interaction Theory of Balanced Charges....Pages 323-372 Relation to Quantum Mechanical Models and Phenomena....Pages 373-387 The Theory of Electromagnetic Interaction of Dressed Charges....Pages 389-404 Comparison of EM Aspects of Dressed and Balanced Charges Theories....Pages 405-420 Front Matter....Pages 421-421 Introduction....Pages 423-425 The Dirac Equation....Pages 427-429 Basics of Spacetime Algebra (STA)....Pages 431-439 The Dirac Equation in the STA....Pages 441-451 The Basics of the Neoclassical Theory of Charges with Spin 1/2....Pages 453-460 Neoclassical Free Charge with Spin....Pages 461-469 Neoclassical Solutions: Interpretation and Comparison with the Dirac Theory....Pages 471-475 Clifford and Spacetime Algebras....Pages 477-489 Multivector Calculus....Pages 491-498 Relativistic Concepts in the STA....Pages 499-517 Electromagnetic Theory in the STA....Pages 519-525 The Wave Function and Local Observables in the STA....Pages 527-530 Multivector Field Theory....Pages 531-538 Front Matter....Pages 539-539 Trajectories of Concentration....Pages 541-612 Energy Functionals and Nonlinear Eigenvalue Problems....Pages 613-639 Front Matter....Pages 641-641 Elementary Momentum Equation Derivation for NKG....Pages 643-644 Fourier Transforms and Green Functions....Pages 645-646 Splitting of a Field into Gradient and Sphere-Tangent Parts....Pages 647-649 Hamilton–Jacobi Theory....Pages 651-655 Point Charges in a Spatially Homogeneous Electric Field....Pages 657-659 Front Matter....Pages 641-641 Statistical and Wave Viewpoints in Hamilton–Jacobi Theory....Pages 661-663 Almost Periodic Functions and Their Time-Averages....Pages 665-667 Vector Formulas....Pages 669-670 The Helmholtz Decomposition....Pages 671-674 Gaussian Wave Packets....Pages 675-677 Back Matter....Pages 679-696 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- orentz 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- ohm theory, this work is completely self-contained 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