  We study the Ward-Takahashi identities in the standard model with the gauge
fixing terms given by (1.1) and (1.2). We find that the isolated singularities
of the propagators for the unphysical particles are poles of even order, not
the simple poles people have assumed them to be. Furthermore, the position of
these poles are ultraviolet divergent. Thus the standard model in the alpha
gauge in general, and the Feynman gauge in particular, is not renormalizable.
We study also the case with the gauge fixing terms (1.3), and find that the
propagators remain non-renormalizable. The only gauge without these
difficulties is the Landau gauge. One therefore has to make a distinction
between the renormalizability of the Green functions and that of the physical
scattering amplitudes.
