In this talk, based on a detailed symmetry analysis, I will state the general rules to build up the effective low energy field theory describing a system of electrons weakly interacting with the lattice degrees of freedom. The basic elements in the construction are the invariant tensors that keep track of the microscopic discrete symmetries into the coarse-grained action. The approach can be applied to lattice systems in arbitrary dimensions and in a systematic way to any desired order in derivatives. I will show the application of the method to the honeycomb lattice and re-obtain the well-known effective action for graphene, containing Dirac fermions coupled to a fictitious gauge field. The talk is based on the results of arXiv:1303.3442