The classical point electron in Colombeau's theory of nonlinear generalized functions
- Independent Scientific Research Institute, Oxford OX4 4YS (United Kingdom)
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 {delta}{sup 2}-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 {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.
- OSTI ID:
- 21175673
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 10 Vol. 49; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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