The classical point-electron in Colombeau's theory of nonlinear generalized functions

Simple item page
dc.creatorGsponer, Andre
dc.date2008-06-30
dc.date2008-11-19
dc.date.accessioned2026-07-07T10:19:03Z
dc.date.available2026-07-07T10:19:03Z
dc.descriptionThe 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 insuring that the electron-singularity is stable, the mass and the spin are diverging integrals of delta-squared-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 one. The most striking result, however, is that the electric and magnetic fields differ from the classical monopolar and dipolar fields by delta-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.
dc.description30 pages. Final published version with a few minor corrections
dc.identifierhttps://arxiv.org/abs/0806.4682
dc.identifierhttp://arxiv.org/abs/0806.4682
dc.identifierJ. Math. Phys., Vol.49 (2008) 102901 (22 pages)
dc.identifierdoi:10.1063/1.2982236
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174368
dc.subjectMathematical Physics
dc.titleThe classical point-electron in Colombeau's theory of nonlinear generalized functions
dc.typetext

Files

Collections

arXiv