I discuss a cold-atoms set-up able to simulate (3+1) Dirac fermions and some applications, relevant both in elementary particle and in condensed matter physics. I show in particular the possibility to add a tunable mass by using Bragg pulses, an effective external electromagnetic coupling and an internal interaction, also covariant.
Finally I consider the 2D limit, describing the emergence of (2+1) Dirac fermions in presence of a strongly anisotropic lattice.