Symmetry-based approach to electron-phonon interactions in graphene

We use the symmetries of monolayer graphene to write a set of constraints that must be satisfied by any electron-phonon interaction hamiltonian. The explicit solution as a series expansion in the momenta gives the most general, model-independent couplings between electrons and long wavelength acoustic and optical phonons. As an application, the possibility of describing elastic strains in terms of effective electromagnetic fields is considered in detail, with an emphasis on group theory conditions and the role of time reversal symmetry.