Axial anomaly on a momentum lattice.

Abstract

We study the axial anomaly in a noncompact formulation on a momentum lattice. We compute the continuum limit for the one-loop diagram from {ital k}-lattice perturbation theory. Starting from {ital k}-lattice regularization, we obtain the standard result for the axial anomaly, if we renormalize by introducing nonlocal subtractions which correspond to nonlocal Lagrangian counterterms. In the worst case this could imply that perturbative renormalization would require an infinite number of counterterms; i.e., it would be nonrenormalizable perturbatively. We have undertaken this study in order to investigate properties of {ital k}-lattice regularization and in particular to exhibit the nonlocalities. We consider this as a starting point in the search for a nonperturbative renormalization scheme, spurred in particular by the recent ideas of Wilson and co-workers on the renormalization of infrared singularities of light-cone field theories, using nonlocal counterterm functions.