  We obtain the Ward identities and the gauge-dependence of Green's functions
in non-Abelian gauge theories by using only the canonical commutation relations
and the equations of motion for the Heisenberg operators. The consideration is
applicable to theories both with and without spontaneous symmetry breaking. We
present a definition of a generalized statistical average which ensures that
the Fourier images of temperature Green's functions of the Fermionic fields
have only even-valued frequencies. This makes it possible to set up a procedure
of gauge-invariant statistical averaging in terms of the Hamiltonian and the
field operators.
