Absence of species doubling in finite-element quantum electrodynamics

In this Letter, it will be demonstrated explicitly that the finite-element formulation of quantum electrodynamics is free from fermion doubling. We do this by (1) examining the lattice fermion propagator and using it to compute the one-loop vacuum polarization on the lattice, and (2) by an explict computation of vector and axial-vector current anomalies for an arbitrary rectangular lattice in the Schwinger model. There it is shown that requiring that the vector current be conserved necessitates the use of a square lattice, in which case the axial-vector current is anomalous.