  The effective action induced by chiral fermions can be written, formally, as
an overlap of two states. These states are the Fock ground states of
Hamiltonians for fermions in even dimensional space with opposite sign mass
terms coupled to identical static vector potentials. A perturbative analysis of
the overlap in the continuum framework produces the correct anomaly for Abelian
gauge fields in two dimensions. When a lattice transfer matrix formalism is
applied in the direction perpendicular to a domain wall on which chiral
fermions live a lattice version of the overlap is obtained. The real part of
the overlap is nonperturbatively defined and previous work indicates that the
real part of the vacuum polarization tensor in four dimensions has the correct
continuum limit for a chiral theory. The phase of the overlap represents the
imaginary part of the chiral action and suffers from ambiguities.
