Two-dimensional lattice with electromagnetic gauge field and fermions included

In this work we deal with the inclusion of fermions on a 2-dimensional lattice with electromagnetic field as the gauge field. We have improved a previous work by introducing explicitly the Dirac gamma matrices in the fermionic determinant and by testing gauge invariance of others terms that appear in the integrals. We find that gauge invariance is preserved, which in turn means that no Itô terms are needed in the effective continuum action.