Klein-Gordon equation from Maxwell-Lorentz dynamics
Abstract
We consider Maxwell-Lorentz dynamics: that is to say, Newton's law under the action of a Lorentz's force which obeys the Maxwell equations. A natural class of solutions are those given by the Lagrangian submanifolds of the phase space when it is endowed with the symplectic structure modified by the electromagnetic field. We have found that the existence of this type of solution leads us directly to the Klein-Gordon equation as a compatibility condition. Therefore, surprisingly, quite natural assumptions on the classical theory involve a quantum condition without any process of limit. This result could be a partial response to the inquiries of Dirac.
Cite
@article{arxiv.1201.5685,
title = {Klein-Gordon equation from Maxwell-Lorentz dynamics},
author = {Ricardo J. Alonso-Blanco},
journal= {arXiv preprint arXiv:1201.5685},
year = {2012}
}
Comments
8 pages; some misprints corrected; added some coments in the abstract and also explaining the relationship with the work of P.A.M. Dirac; also added 2 references