A PERTURBATIVE CONSTRUCTION OF LATTICE CHIRAL FERMIONS

We perform a renormalization group transformation to construct perturb atively a lattice theory of chiral fermions. The field variables of th e continuum theory are averaged over hypercubes to define lattice fiel ds, Integrating out the continuum variables we derive a chirally invar iant effective action for the lattice fields. This is consistent with the Nielsen-Ninomiya theorem because the effective action is nonlocal. We also construct the axial current on the lattice and we show that t he axial anomaly of the continuum theory is reproduced in the Schwinge r model.