THE EQUIVALENCE OF TWO TRANSFORMATIONS OF THE INVARIANCE OF LAGRANGIAN FUNCTION IN NON-ABELIAN GAUGE FIELD

In this paper,the general transformation of non-abelian gauge field is derived from the in variance reguirement of the effective lagrangian function.It is shown that when the group parameter θ(x) is the product of the anti-commuting ghost field and an infinitesimal number anticommuting ξ which is independent of the component indices space,the B.R.S.transformation is obtained.When θ(x) is equal to the ghost field C(x) times an infinitesimal tensor ξ_i which is commuting with respect to the upper index b,we get another transformation.Both transformations are proved to be equivalent.