  Based on a detailed symmetry analysis, we 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 our
construction are what we call the "memory tensors", that keep track of the
microscopic discrete symmetries into the coarse-grained action. The present
approach can be applied to lattice systems in arbitrary dimensions and in a
systematic way to any desired order in derivatives. We apply the method to the
honeycomb lattice and re-obtain the by now well-known effective action of Dirac
fermions coupled to fictitious gauge fields. As a second example, we derive the
effective action for electrons in the kagom\'e lattice, where our approach
allows to obtain in a simple way the low energy electron-phonon coupling terms.
