  A new way to write the massive scalar and fermion propagators on a background
of a weak gauge field is presented. They are written in a form that is
manifestly gauge-covariant up to several additional terms that can be written
as boundary terms in momentum space. These additional terms violate
Ward-Takahashi identities and need to be renormalized by appropriate
counterterms if the complete theory is to be gauge-covariant. This form makes
it possible to calculate many amplitudes in a manifestly gauge-covariant way
(at the same time reducing the number of Feynman diagrams). It also allows to
express some counterterms in a way independent of the regularization scheme and
provides an easy way to derive the anomalous term affecting the chiral current
conservation.
