Explicit currents in SU(5) andE7unified gauge theories

Explicit currents generating the SU(5) and ${\mathrm{E}}_7$ Lie Algebras are constructed out of the quark and lepton fields appearing in the appropriate representations of these groups. The diquark-leptoquark structure of the currents involved in baryon-lepton transitions is exhibited, and it is pointed out that the diquark currents are related to color and flavor currents through Pauli-Gürsey transformations. In the SU(5) case, the $u$ and $d$ quarks are found to have charges $+\frac{2}{3}$ and $-\frac{1}{3}$, respectively, as an inevitable result of the way SU(2) × U(1) is embedded in SU(5). The ${\mathrm{E}}_7$ currents are obtained by using Majorana leptons which can be related to Weyl leptons through an SU(6) generalization of the Pauli-Gürsey transformations. The dependence of diquark charges and algebra upon the assumed statistics for the basic quark and lepton fields is also discussed.