Nonlinear Theory of Fields

Abstract

Suggested modification of the Einstein-Maxwell system, such that Maxwell equations become non-gauge and nonlinear. The theory is based on assumption that observable (i.e., felt by particles) metric is $ {\tilde{g}}_{ab} = g_{ab} - l^2{A}_a{A}_b$, where $g_{ab}$ is metric (found from Einstein equations), $A_a$ is electromagnetic potential, and $l$ is fundamental constant of the theory. Specific model of the mass and charge densities of a fundamental particle is considered. As a result, one obtains solutions corresponding to quantized electrical charge with spectrum $q_{n} = {{2n}\over3}e$ and $q'_{n} = -{(2n+1)\over3}e$, where $n = 0, 1, 2, ...$ Theory predicts Coulomb interaction between electrical charges and masses. Namely, if ($m, e$) and ($m',e'$) describe masses and electrical charges of two particles respectively, then energy of interaction (in non-relativistic limit) is $V(r) = [ee' - kmm' - \sqrt k(em' + e'm)]/r$. It follows, then, that the Earth's mass, $M_E$, contributes negative electrical charge, $Q_E = - \sqrt k M_E$, which explains why primary cosmic rays consist mainly of positively charged particles. One may attribute the fairweather electric field at the Earth's surface to the charge $Q_E$.