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Journal of Mathematical Physics : The classical point electron in Colombeaus theory of nonlinear generalized functions

By Andre Gsponer

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Book Id: WPLBN0002169551
Format Type: PDF eBook :
File Size: Serial Publication
Reproduction Date: 1 October 2008

Title: Journal of Mathematical Physics : The classical point electron in Colombeaus theory of nonlinear generalized functions  
Author: Andre Gsponer
Volume: Issue : October 2008
Language: English
Subject: Science, Physics, Natural Science
Collections: Periodicals: Journal and Magazine Collection, Journal of Mathematical Physics Collection
Historic
Publication Date:
Publisher: American Institute of Physics

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Gsponer, A. (n.d.). Journal of Mathematical Physics : The classical point electron in Colombeaus theory of nonlinear generalized functions. Retrieved from http://community.worldlibrary.net/


Description
Description: The electric and magnetic fields of a pole-dipole singularity attributed to a point-electron singularity in the Maxwell field are expressed in a Colombeau algebra of generalized functions. This enables one to calculate dynamical quantities quadratic in the fields which are otherwise mathematically ill-defined: the self-energy (i.e., “mass”), the self-angular momentum (i.e., “spin”), the self-momentum (i.e., “hidden momentum”), and the self-force. While the total self-force and self-momentum are zero, therefore ensuring that the electron singularity is stable, the mass and spin are diverging integrals of δ2-functions. Yet, after renormalization according to standard prescriptions, the expressions for mass and spin are consistent with quantum theory, including the requirement of a gyromagnetic ratio greater than 1. The most striking result, however, is that the electric and magnetic fields differ from the classical monopolar and dipolar fields by δ-function terms which are usually considered as insignificant, while in a Colombeau algebra these terms are precisely the sources of the mechanical mass and spin of the electron singularity.

 

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