  In this work we present an optical lattice setup to realize a full Dirac
Hamiltonian in 2+1 dimensions. We show how all possible external potentials
coupled to the Dirac field can arise from perturbations of the existing
couplings of the honeycomb lattice model, without the need of additional laser
fields. This greatly simplifies the proposed implementations, requiring only
spatial modulations of the intensity of the laser beams. We finally suggest
several experiments to observe the properties of the Dirac field in the setup.
