Perturbation theory for undoubled lattice fermions

Abstract

I study a class of lattice versions of QED with fermions with the aim of clarifying the relationship between the fermion spectrum (doubled or not), continuous chiral symmetry, the range of the lattice interactions, and the validity of perturbation theory. Theories of this class with an undoubled spectrum, such as the formulation due to Drell, Weinstein, and Yankielowicz (DWY), have infinite-range interactions and infrared-divergent perturbation series. The infrared singularities can be removed by a resummation of the series. I then carry out a renormalization program for DWY QED after which the $a\to 0$ limit of the theory is finite and coincides with continuum QED. Finally, I consider the nonperturbative structure of DWY QED.