Electromagnetic Field Theory without Divergence Problems 2. A Least Invasively Quantized Theory

Abstract

The classical Maxwell--Born--Infeld field equations coupled with a Hamilton--Jacobi law of point charge motion are partially quantized by coupling the Hamilton-Jacobi phase function with an amplitude function, which combines with the phase function into a single complex wave function satisfying a relativistic Klein--Gordon equation self-consistently coupled to the evolution equations for the electromagnetic fields with generic point source (explicitly worked out for one particle; options for many particles briefly discussed). Radiation-free stationary states exist. The hydrogen spectrum with infinitely massive nucleus is discussed in some detail and upper estimates for Born's `aether constant' obtained. In the nonrelativistic limit the model reduces to the de-Broglie--Bohm formulation of quantum mechanics.

Corrections at galley stage incorporated (mostly minor corrections, except for a blunder in the estimate of the error term U to the Coulomb interaction) 38p; to appear in JSP vol. 116, issue dedicated to Elliott H. Lieb on his 70th birthday. Part I is math-ph/0306076

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Cited by in corpus (15)

• The "Unromantic Pictures" of Quantum Theory
• Nonperturbative calculation of Born-Infeld effects on the Schroedinger spectrum of the hydrogen atom
• Electromagnetic field theory without divergence problems: 1. The Born Legacy
• 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 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
• 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
• Derivation of the magnetic Euler-Heisenberg energy
• Non-existence of multiple-black-hole solutions close to Kerr-Newman
• Exact self-similar solutions in Born-Infeld theory
• Weak second Bianchi identity for static, spherically symmetric spacetimes with timelike singularities
• The Einstein-Infeld-Hoffmann legacy in mathematical relativity II. Quantum laws of motion