The system of equations describing 4 generations with the symmetry group SU (3) C × SU (2) L × U (1)

Abstract

The system of 16-component equations including two equations of the Bethe-Salpeter kind (without an interaction) and two additional conditions are considered. It is shown that the group of the initial symmetry is SU (3)C × SU (2)L × U (1). The symmetry group is established as the consequence of the field equations; SU (2) should be chiral, the color space has the signature (+ + −). The structure of permissible multiplets of the group coincides with the one postulated in the SU (3)C × SU (2)L -model of strong and electroweak interactions excluding the possible existence of the additional SU (2)R -singlet in a generation.