Neoclassical Theory of Electromagnetic Interactions

1. Introduction
Anatoli Babin, Alexander Figotin

2. The History of Views on Charges, Currents and the Electromagnetic Field
Anatoli Babin, Alexander Figotin

3. The Neoclassical Field Theory of Charged Matter: A Concise Presentation
Anatoli Babin, Alexander Figotin

Part I. Classical Electromagnetic Theory and Special Relativity

4. The Maxwell Equations
Anatoli Babin, Alexander Figotin

5. Dipole Approximation for Localized Distributed Charges
Anatoli Babin, Alexander Figotin

6. The Minkowski Four-Dimensional Spacetime and Relativistic Kinematics
Anatoli Babin, Alexander Figotin

7. Longitudinal and Transversal Fields
Anatoli Babin, Alexander Figotin

8. Non-relativistic Quasistatic Approximations
Anatoli Babin, Alexander Figotin

9. Electromagnetic Field Lagrangians
Anatoli Babin, Alexander Figotin

Part II. Classical Field Theory

10. Variational Principles, Lagrangians, Field Equations and Conservation Laws
Anatoli Babin, Alexander Figotin

11. Lagrangian Field Formalism for Charges Interacting with EM Fields
Anatoli Babin, Alexander Figotin

12. Lagrangian Field Formalism for Balanced Charges
Anatoli Babin, Alexander Figotin

13. Lagrangian Field Formalism for Dressed Charges
Anatoli Babin, Alexander Figotin

Part III. The Neoclassical Theory of Charges

14. Rest and Time-Harmonic States of a Charge
Anatoli Babin, Alexander Figotin

15. Uniform Motion of a Charge
Anatoli Babin, Alexander Figotin

16. Accelerating Wave-Corpuscles
Anatoli Babin, Alexander Figotin

17. Interaction Theory of Balanced Charges
Anatoli Babin, Alexander Figotin

18. Relation to Quantum Mechanical Models and Phenomena
Anatoli Babin, Alexander Figotin

19. The Theory of Electromagnetic Interaction of Dressed Charges
Anatoli Babin, Alexander Figotin

20. Comparison of EM Aspects of Dressed and Balanced Charges Theories
Anatoli Babin, Alexander Figotin

Part IV. The Neoclassical Theory of Charges with Spin

21. Introduction
Anatoli Babin, Alexander Figotin

22. The Dirac Equation
Anatoli Babin, Alexander Figotin

23. Basics of Spacetime Algebra (STA)
Anatoli Babin, Alexander Figotin

24. The Dirac Equation in the STA
Anatoli Babin, Alexander Figotin

25. The Basics of the Neoclassical Theory of Charges with Spin 1/2
Anatoli Babin, Alexander Figotin

26. Neoclassical Free Charge with Spin
Anatoli Babin, Alexander Figotin

27. Neoclassical Solutions: Interpretation and Comparison with the Dirac Theory
Anatoli Babin, Alexander Figotin

28. Clifford and Spacetime Algebras
Anatoli Babin, Alexander Figotin

29. Multivector Calculus
Anatoli Babin, Alexander Figotin

30. Relativistic Concepts in the STA
Anatoli Babin, Alexander Figotin

31. Electromagnetic Theory in the STA
Anatoli Babin, Alexander Figotin

32. The Wave Function and Local Observables in the STA
Anatoli Babin, Alexander Figotin

33. Multivector Field Theory
Anatoli Babin, Alexander Figotin

Part V. Mathematical Aspects of the Theory of Distributed Elementary Charges

34. Trajectories of Concentration
Anatoli Babin, Alexander Figotin

35. Energy Functionals and Nonlinear Eigenvalue Problems
Anatoli Babin, Alexander Figotin

Part VI. Appendices

36. Elementary Momentum Equation Derivation for NKG
Anatoli Babin, Alexander Figotin

37. Fourier Transforms and Green Functions
Anatoli Babin, Alexander Figotin

38. Splitting of a Field into Gradient and Sphere-Tangent Parts
Anatoli Babin, Alexander Figotin

39. Hamilton–Jacobi Theory
Anatoli Babin, Alexander Figotin

40. Point Charges in a Spatially Homogeneous Electric Field
Anatoli Babin, Alexander Figotin

41. Statistical and Wave Viewpoints in Hamilton–Jacobi Theory
Anatoli Babin, Alexander Figotin

42. Almost Periodic Functions and Their Time-Averages
Anatoli Babin, Alexander Figotin

43. Vector Formulas
Anatoli Babin, Alexander Figotin

44. The Helmholtz Decomposition
Anatoli Babin, Alexander Figotin

45. Gaussian Wave Packets
Anatoli Babin, Alexander Figotin

Keywords: Mathematics, Partial Differential Equations, Mathematical Applications in the Physical Sciences, Mathematical Methods in Physics, Optics and Electrodynamics, Elementary Particles, Quantum Field Theory, Nonlinear Dynamics