The classical point-electron in the sequence algebra (C^infinity)^I

TL;DR

This paper compares the calculation of a classical point-electron's properties in Colombeau algebra and regularized distributions, highlighting the advantages of Colombeau theory for handling nonlinear products of distributions.

Contribution

It demonstrates that Colombeau algebra provides exact calculations of electron mass and spin as squares of delta-functions, unlike the approximate results in traditional frameworks.

Findings

Colombeau algebra yields exact integrals of delta-function squares.

Traditional regularized distributions provide only approximate results.

Colombeau theory may be physically preferable for nonlinear distribution products.

Abstract

In arXiv:0806.4682 the self-energy and self-angular momentum (i.e., electromagnetic mass and spin) of a classical point-electron were calculated in a Colombeau algebra. In the present paper these quantities are calculated in the better known framework of `regularized distributions,' i.e., the customary setting used in field-theory to manipulate diverging integrals, distributions, and their products. The purpose is to compare these two frameworks, and to highlight the reasons why the Colombeau theory of nonlinear generalized functions could be the physically preferred setting for making these calculations. In particular, it is shown that, in the Colombeau algebra, the point-electron's mass and spin are {exact} integrals of squares of delta-functions, whereas this is only an approximation in the customary framework.