Extending Lehnert’s Revised Quantum Electrodynamics to Fractal Media & Cantor Sets

Abstract

In a series of papers, Bo Lehnert proposed a novel and revised version of quantum electrodynamics (RQED) based on Proca equations. However, as far as I know there is no paper yet for extending RQED to fractal media and Cantor Sets. Drawing similarity between Proca and Maxwell equations, I extend RQED further in the present paper based on a recent paper by Zhao et al. derived Maxwell equations on Cantor sets from local fractional vector calculus. It can be shown that Maxwell equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. I also extend RQED to anisotropic fractal media based on the work of Martin Ostoja-Starzewski. It is hoped that this paper may stimulate further investigations and experiments for finding physics beyond Standard Model in fractal media. It may be expected to have some impact to fractal cosmology modeling too.