On the Charges and Currents in the Quantum Field Theory

Abstract

This paper is concerned with the determination of currents and charges in hypercomplex extensions of the Feynman-Dyson derivation of the Maxwell-Faraday equations. We analyze the appearance of charges and currents in non-Abelian versions of that approach: SU(2), SU(3) and G2. The structure constants of G2 Lie algebra are computed explicitly. Finally, we suggest a seven-dimensional treatment of color.