On quantization of mass and electrical charge

Abstract

Suggested non-linear, non-gauge modification of the Maxwell theory of electromagnetism based on correlation between electromagnetic potential, $A_a$, and metric, $g_{ab}$, such that tensor $G_{ab} = g_{ab} - l^2{A}_a{A}_b$ represents observable metric. Here $l$ is fundamental constant of the theory. The idea, that the charge density of elementary particle could be a function of electromagnetic potential and background metric (only) is accepted, and specific model of the density is considered. Due to non-linearity of equations, one obtains solutions corresponding to quantized electrical charge with spectrum $q_{n} = {{2n}\over3}e$ and $q'_{n} = -{(2n+1)\over3}e$, where $n = 0, 1, 2, ...$