A nonlinear relativistic approach to mathematical representation of vacuum electromagnetism based on extended Lie derivative

Abstract

This paper presents an alternative {\it relativistic nonlinear} approach to the vacuum case of classical electrodynamics. Our view is based on the understanding that the corresponding differential equations should be dynamical in nature. So, they must represent local energy-momentum balance relations. Formally, the new equations are in terms of appropriately extended Lie derivative of $\mathbb{R}^2$-valued differential 2-form along a $\mathbb{R}^2$-valued 2-vector on Minkowski space-time.