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

TL;DR

This paper introduces a novel least invasively quantized electromagnetic field theory that combines classical Maxwell--Born--Infeld equations with quantum mechanics, leading to a self-consistent relativistic model with stationary states and hydrogen spectrum analysis.

Contribution

It develops a new quantization approach for electromagnetic fields coupled with point charges, integrating Klein--Gordon dynamics with classical field equations.

Findings

Existence of radiation-free stationary states

Analysis of hydrogen spectrum with an infinitely massive nucleus

Model reduces to de-Broglie--Bohm quantum mechanics in the nonrelativistic limit

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.