Hadamard-Finite-Part simultaneous infrared and ultraviolet self-regularization of Universal functions in electrostatic limit

Divergences in theoretical and computational electromagnetics, or more generally in computational and mathematical physics, can be fascinating and intimidating at the same time. Therefore, it is imperative to understand the genesis of various divergences and develop a unified theory for their treatment. An in-depth analysis of the semantic employed in the contemporary laws of electrostatic, electrodynamics, gravitation theory, Quantum Field Theory and particle physics reveals astonishing similarity amongst various notions of divergences and their regularization and renormalization techniques. In particular in QFT the two most prominent ones are ultraviolet divergences (those associated with large values of momenta (wavenumber); i.e., short wavelengths, hence ultraviolet, and infrared divergences, those associated with small momenta (wavenumber); i.e., large wavelengths, hence infrared. In this contribution, two major results are proven, by considering the solution of Poisson equation in terms of two-dimensional oscillatory integrals: (i) Application of the Method of Moments automatically leads to Hadamard-Finite-Part UV self-regularization, (ii) without deteriorating the field behavior in IR region. (iii) Geometry-independent Universal functions are constructed for the MoMs applications.