Staggered fermions and chiral-symmetry breaking in transverse lattice regulated QED

Staggered fermions are constructed for the transverse lattice regularization scheme. The weak perturbation theory of transverse lattice noncompact QED is developed in the light-cone gauge, and we argue that for fixed lattice spacing this theory is ultraviolet finite, order by order in perturbation theory. However, by calculating the anomalous scaling dimension of the link fields, we find that the interaction Hamiltonian becomes nonrenormalizable for $g^2\mathrm{}\left(a\right)>4\mathrm{}\pi$,where $g\left(a\right)\mathrm{}$ is the bare (lattice) QED coupling constant. We conjecture that this is the critical point of the chiral-symmetry-breaking phase transition in QED. Nonperturbative chiral-symmetry breaking is then studied in the strong-coupling limit. The discrete remnant of chiral symmetry that remains on the lattice is spontaneously broken, and the ground state to lowest order in the strong-coupling expansion corresponds to the classical ground state of the two-dimensional spin-½ Heisenberg antiferromagnet.