  Feynman rules for the vacuum amplitude of fermions coupled to external gauge
and Higgs fields in a domain wall lattice model are derived using
time--dependent perturbation theory. They have a clear and simple structure
corresponding to 1--loop vacuum graphs. Their continuum approximations are
extracted by isolating the infrared singularities and it is shown that, in each
order, they reduce to vacuum contributions for chiral fermions. In this sense
the lattice model is seen to constitute a valid regularization of the continuum
theory of chiral fermions coupled to weak and slowly varying gauge and Higgs
fields. The overlap amplitude, while not gauge invariant, exhibits a well
defined (modulo phase conventions) response to gauge transformations of the
background fields. This response reduces in the continuum limit to the expected
chiral anomaly, independently of the phase conventions.
