Gauge invariance of spontaneously broken non-Abelian theories in the Bogolyubov–Parasyuk–Hepp–Zimmermann method

The Bogolyubov–Parasyuk–Hepp regularization procedure in Zimmermann's formulation is applied to non-Abelian gauge theories with spontaneously broken symmetry. Ward identities for the Green's function are proved in a general gauge. Gauge invarianee of the elements of the $S$-matrix of physical particles follows from the Ward identities. The proof that the $S$-matrix is gauge invariant is considered in detail for a Yang–Mills massless field.