Electromagnetic field theory without divergence problems: 1. The Born Legacy

Abstract

A fully consistent classical relativistic electrodynamics with spinless point charges is constructed. The classical evolution of the electromagnetic fields is governed by the nonlinear Maxwell--Born--Infeld field equations, the classical evolution of the point charges by a many-body Hamilton--Jacobi law of motion. The Pauli principle for bosons can be incorporated in the classical Hamilton--Jacobi formalism. The Cauchy problem is explained and illustrated with examples. The question of charge-free field solitons is addressed also and it is shown that if they exist, their peak field strengths must be enormous. The value The value of Born's constant is shown to be a subtle open issue.

Minor corrections at galley stage incorporated. 66p; to appear in JSP vol. 116, issue dedicated to Elliott H. Lieb on his 70th birthday. Part II is math-ph/0311034

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Cited by in corpus (22)

• The "Unromantic Pictures" of Quantum Theory
• Nonperturbative calculation of Born-Infeld effects on the Schroedinger spectrum of the hydrogen atom
• On the Quasi-Linear Elliptic PDE $-\nabla \cdot (\nabla u/\sqrt{1-|\nabla u{|}^2})=4\pi {\sum }_k{a}_k{\delta }_{s_k}$ in Physics and Geometry
• The Nonlinear Stability of the Trivial Solution to the Maxwell-Born-Infeld System
• The force on a point charge source of the classical electromagnetic field
• The Global Stability of the Minkowski Spacetime Solution to the Einstein-Nonlinear Electromagnetic System in Wave Coordinates
• Approximate Born-Infeld Effects on the Relativistic Hydrogen Spectrum
• Electromagnetic Field Theory without Divergence Problems 2. A Least Invasively Quantized Theory
• On the Static Spacetime of a Single Point Charge
• The Vlasov limit and its fluctuations for a system of particles which interact by means of a wave field
• Microscopic foundations of kinetic plasma theory: The relativistic Vlasov--Maxwell equations and their radiation-reaction-corrected generalization
• Some uniqueness results for stationary solutions to the Maxwell-Born-Infeld field equations and their physical consequences
• On Radiation Reaction in Classical Electrodynamics
• Convergent perturbative power series solution of the stationary Maxwell--Born--Infeld field equations with regular sources
• Misleading signposts along the de Broglie-Bohm road to quantum mechanics
• Ground State H-Atom in Born-Infeld Theory
• Non-existence of multiple-black-hole solutions close to Kerr-Newman
• Constructing graphs over $R^n$ with small prescribed mean-curvature
• Exact self-similar solutions in Born-Infeld theory
• Derivation of the magnetic Euler-Heisenberg energy
• Existence and regularity for prescribed Lorentzian mean curvature hypersurfaces, and the Born-Infeld model
• Weak second Bianchi identity for static, spherically symmetric spacetimes with timelike singularities