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We consider the relationship between the tight-binding Hamiltonian of thetwo-dimensional honeycomb lattice of carbon atoms with nearest neighbor hoppingonly and the 2+1 dimensional Hamiltonian of quantum electrodynamics whichfollows in the continuum limit. We pay particular attention to the symmetriesof the free Dirac fermions including spatial inversion, time reversal, chargeconjugation and chirality. We illustrate the power of such a mapping byconsidering the effect of the possible symmetry breaking which corresponds tothe creation of a finite Dirac mass, on various optical properties. Inparticular, we consider the diagonal AC conductivity with emphasis on how thefinite Dirac mass might manifest itself in experiment. The optical sum rulesfor the diagonal and Hall conductivities are discussed.

AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics