  Staggered fermions are constructed for the transverse lattice regularization
scheme. The weak perturbation theory of transverse lattice non-compact QED is
developed in 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 non-renormalizable for $g^2(a) > 4\pi$,
where $g(a)$ is the bare (lattice) QED coupling constant. We conjecture that
this is the critical point of the chiral symmetry breaking phase transition in
QED. Non-perturbative 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 one-half Heisenberg antiferromagnet.
