The classical point - electron in the sequence algebra ( C ∞ ) I Andre

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 pointelectron’s mass and spin are exact integrals of squares of delta-functions, whereas this is only an approximation in the customary framework.