  We consider the relationship between the tight-binding Hamiltonian of the
two-dimensional honeycomb lattice of carbon atoms with nearest neighbor hopping
only and the 2+1 dimensional Hamiltonian of quantum electrodynamics which
follows in the continuum limit. We pay particular attention to the symmetries
of the free Dirac fermions including spatial inversion, time reversal, charge
conjugation and chirality. We illustrate the power of such a mapping by
considering the effect of the possible symmetry breaking which corresponds to
the creation of a finite Dirac mass, on various optical properties. In
particular, we consider the diagonal AC conductivity with emphasis on how the
finite Dirac mass might manifest itself in experiment. The optical sum rules
for the diagonal and Hall conductivities are discussed.
