Discrete symmetry in graphene: the Dirac equation and beyond

In this paper we review the discrete symmetries of the Dirac equation using elementary tools, but in a comparative order: the usual 3 + 1 dimensional case and the 2+1 dimensional case. Motivated by new applications of the 2d Dirac equation in condensed matter (e.g. graphene), we further analyze the discrete symmetries of a full tight-binding model in hexagonal lattices without conical approximations. We touch upon an effective CPT symmetry breaking that occurs when deformations and second-neighbor corrections are considered.