N. Sadooghi et Hj. Rothe, CONTINUUM BEHAVIOR OF LATTICE QED, DISCRETIZED WITH ONE-SIDED LATTICEDIFFERENCES, IN ONE-LOOP ORDER, Physical review. D. Particles and fields, 55(11), 1997, pp. 6749-6759
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.