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 illdefined: The self-energy (i.e., ‘mass’), the self-angular momentum (i.e., ‘spin’), the self-mom...

We present a geometric approach to deening an algebra ^ G(M) (the Colombeau algebra) of generalized functions on a smooth manifold M containing the space D 0 (M) of distributions on M. Based on diierential calculus in convenient vector spaces we achieve an intrinsic construction of ^ G(M). ^ G(M) is a diierential algebra, its elements possessing Lie derivatives with respect to arbitrary smooth ...

We present a geometric approach to deening an algebra ^ G(M) (the Colombeau algebra) of generalized functions on a smooth manifold M containing the space D 0 (M) of distributions on M. Based on diierential calculus in convenient vector spaces we achieve an intrinsic construction of ^ G(M). ^ G(M) is a diierential algebra, its elements possessing Lie derivatives with respect to arbitrary smooth ...

The electromagnetic field of the ultrarelativistic Reissner Nordstrøm Solution shows the physically highly unsatisfactory property of a vanishing field tensor but a nonzero, i.e. δ-like, energy density. The aim of this work is to analyse this situation from a mathematical point of view, using the framework of Colombeau’s theory of nonlinear generalized functions. It is shown that the physically...

A new approach to the algebra Gτ of temperate nonlinear generalized functions is proposed, in which Gτ is based on the space OM endowed with is natural topology in contrary to previous constructions. Thus, this construction fits perfectly in the general scheme of construction of Colombeau type algebras and reveals better properties of Gτ . This is illustrated by the natural introduction of a re...

We investigate homogeneity in the special Colombeau algebra on Rd as well as on the pierced space Rd \ {0}. It is shown that strongly scaling invariant functions on Rd are simply the constants. On the pierced space, strongly homogeneous functions of degree α admit tempered representatives, whereas on the whole space, such functions are polynomials with generalized coefficients. We also introduc...

The electromagnetic eld of the ultrarelativistic Reissner Nordstrrm Solution shows the physically highly unsatisfactory property of a vanishing eld tensor but a nonzero, i.e.-like, energy density. The aim of this work is to analyse this situation from a mathematical point of view, using the framework of Colombeau's theory of nonlinear generalized functions. It is shown that the physically unsat...

Extending the construction of the algebra Ĝ(M) of scalar valued Colombeau functions on a smooth manifold M (cf. [4]), we present a suitable basic space for eventually obtaining tensor valued generalized functions on M , via the usual quotient construction. This basic space canonically contains the tensor valued distributions and permits a natural extension of the classical Lie derivative. Its m...