Multidimensional Geometrical Model of the Renormalized Electrical Charge with Splitting off the Extra Coordinates

Abstract

A geometrical model of electric charge is proposed. This model has ``naked'' charge screened with a ``fur - coat'' consisting of virtual wormholes. The 5D wormhole solution in the Kaluza - Klein theory is the ``naked'' charge. The splitting off of the 5D dimension happens on the two spheres (null surfaces) bounding this 5D wormhole. This allows one to sew two Reissner - Nordstr\"om black holes onto it on both sides. The virtual wormholes entrap a part of the electrical flux lines coming into the ``naked'' charge. This effect essentially changes the charge visible at infinity so that it satisfies the real relation $m^2<e^2$.