Electromagnetic Field Theory without Divergence Problems 2. A Least Invasively Quantized Theory
摘要
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.
引用
@article{arxiv.math-ph/0311034,
title = {Electromagnetic Field Theory without Divergence Problems 2. A Least Invasively Quantized Theory},
author = {Michael K. -H. Kiessling},
journal= {arXiv preprint arXiv:math-ph/0311034},
year = {2009}
}
备注
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