  The electrodynamics of a two-dimensional gas of massless fermions in graphene
is studied by a collisionless hydrodynamic approach. A low-energy dispersion
relation for the collective modes (plasmons) is derived both in the absence and
in the presence of a perpendicular magnetic field. The results for graphene are
compared to those for a standard two-dimensional gas of massive electrons. We
further compare the results within the classical hydrodynamic approach to the
full quantum mechanical calculation in the random phase approximation. The
low-energy dispersion relation is shown to be a good approximation at small
wave vectors. The limitations of this approach at higher order is also
discussed.
