  Lattice fermions have well-known difficulties with chiral symmetry. To evade
them it is possible to couple continuum fermions to lattice gauge fields, by
introducing an interpolation of the latter. Following this line of thinking,
this paper presents two Euclidean formulations of the effective action that
appears after functional integration over fermion fields, one for vector-like
and the other for chiral couplings. With suitable finite-mode regulators both
effective actions can be evaluated in a finite computation. The prescriptions
provided here contain some details not found in previous work marrying
continuum fermions to the lattice via an interpolation. For example, the
counter-terms needed to maintain chiral gauge invariance are explicitly given.
By construction coupling-constant renormalization, anomaly structure, and (in
the chiral gauge theory) fermion nonconserving amplitudes all satisfy one's
expectations from perturbative and semi-classical analyses.
