  Recent experiments have proven that the quasiparticles in graphene obey a
Dirac equation. Here we show that microwaves are an excellent probe of their
unusual dynamics. When the chemical potential is small the intraband response
can exhibit a cusp around zero frequency $\Omega$ and this unusual lineshape
changes to Drude-like by increasing the chemical potential $|\mu|$, with width
also increasing linearly with $\mu$. The interband contribution at T=0 is a
constant independent of $\Omega$ with a lower cutoff at $2 \mu$. Distinctly
different behavior occurs if interaction-induced phenomena in graphene cause an
opening of a gap $\Delta$. At large magnetic field $B$, the diagonal and Hall
conductivities at small $\Omega$ become independent of $B$ but remain nonzero
and show structure associated with the lowest Landau level. This occurs because
in the Dirac theory the energy of this level, $E_0 = \pm \Delta$, is field
independent in sharp contrast to the conventional case.
