  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.
