  As a first step towards constructing chiral models on the lattice with
staggered fermions, we study a U(1) model with axial-vector coupling to an
external gauge field in two dimensions. In our approach gauge invariance is
broken, but it is restored in the classical continuum limit. We find that the
continuum divergence relations for the vector and axial-vector currents are
reproduced, up to contact terms, which we determine analytically. The current
divergence relations are also studied numerically for smooth external gauge
fields with topological charge zero. We furthermore investigate the effect of
fluctuating gauge transformations and of gauge configurations with non-trivial
topological charge.
