1. The Restriction Condition of Gauge Transformation Which Motion Equation of Non-Abelian Gauge Field Must Satisfy

Abstracts In the current theory of non-Abelian gauge field, we only claim the invariability of Lagrangian, without claim the invariability of the motion equation. This is inconsistent and irrational. It is proved that a restriction relation between gauge potentials and group parameters must be satisfied in order to ensure the gauge invariability of the motion equation of non-Abelian gauge field, and the restriction relation is equivalent to the Faddeev--Popov theory. The result leads to that the completely local gauge invariability is violated but there still exists the incompletely local gauge invariability. After the restriction relation is considered, the mass item of the non-Abelian gauge fields can be added into the Lagrangian and motion equation directly without violating gauge invariability. The corresponding identity is obtained and the theory is still renormalizable. In this way, the Higgs mechanism becomes unnecessary. It means that we can reach a coincident theory without the hypothesis of the Higgs particles again. The description of the stander theory of particle physics can also be simplified greatly and the problem of violation in strong interaction can also be solved thoroughly