CONTINUUM BEHAVIOR OF LATTICE QED, DISCRETIZED WITH ONE-SIDED LATTICEDIFFERENCES, IN ONE-LOOP ORDER

A lattice action far QED is considered, where the derivatives in the D irac;operator are replaced by one-sided lattice differences. A systema tic expansion in the lattice spacing of the one-loop contribution to t he fermion self-energy, vacuum polarization tensor, and vertex functio n is carried out for an arbitrary choice of one-sided lattice differen ces. It is shown that only the vacuum polarization tensor possesses th e correct continuum limit, while the fermion self-energy and vertex fu nction receive noncovariant contributions. A lattice action, discretiz ed with a fixed choice of one-sided lattice differences, therefore, do es not define a renormalizable field theory. The noncovariant contribu tions can, however, be eliminated by averaging the expression over all possible choices of one-sided lattice differences.