Investigation on the Charges and Currents in the Quantum Field Theory

This paper is concerned with the determination of currents and charges in hypercomplex extensions
of the Feynman–Dyson derivation of the Maxwell–Faraday equations. This paper is a continuation of
the discussions on hypercomplex extensions of the Feynman–Dyson derivation of the Maxwell–
Faraday equations. Usually mathematical proofs have only relatively minor value since for any set of
mathematical arguments it is possible to present an equally valuable set of contra-arguments; in
physics, by contrast, the ultimate verification of a statement is its confirmation by experiment and the
solution is unique.
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.