  An ansatz for the fermion vacuum functional on a lattice is proposed. It is
proved to reproduce correct continuum limit for convergent diagrams of any
finite order in smooth external fields, as well as consistent chiral anomalies,
and ensures gauge invariance of the absolute value of the functional at any
lattice spacing. The ansatz corresponds to a certain non-local fermion action
having global chiral invariance. Problems caused by non-smooth gauge fields are
discussed.
