I will present two new schemes for the simulation of quantum field theory
by ultra-cold fermions on optical lattices. In the first part of my talk I will discuss how to simulate the (3+1)D spin 3/2 massless particle,
starting from the derivation of a consistent hamiltonian for it. I will consider later the inconsistencies related to the
minimal electromagnetic coupling (Velo-Zwanziger paradox) and a strategy to solve it, focusing on the
possibilities to probe this scenario onto an optical lattice device. The second part will be devoted instead to the realization of (non abelian) symmetry-locked phases and of non-abelian fractional vortices, obtained as excitations of their ground states.
These phases turn out to be particularly relevant for the physics of ultra-dense (quark matter) stars.