Solving the gauge Identities

The author shows how one may 'solve' the Ward-Takahashi identities of a gauge theory to determine the longitudinal Green functions in terms of the basic source propagators and in such a way that on-shell amplitudes reduce to their classical values. The method is demonstrated for scalar, spinor and vector sources in Lorentz covariant and non-covariant Abelian gauges; but for non-Abelian groups he works in the axial gauge in order to avoid fictitious terms which otherwise spoil the procedure.