  The electromagnetic response of graphene in a magnetic field is studied, with
particular emphasis on the quantum features of its ground state (vacuum). The
graphene vacuum, unlike in conventional quantum Hall systems, is a dielectric
medium and carries an appreciable amount of electric and magnetic
susceptibilities. The dielectric effect grows rapidly with increasing filling
factor nu in such a way that reflects the 'relativistic' Landau-level
characteristics of graphene as well as its valley and spin degeneracy. A close
look into the dielectric function also reveals that the Coulomb interaction is
efficiently screened on the scale of the magnetic length, leading to a
prominent reduction of the exciton spectra in graphene. In addition, an
effective gauge theory of graphene is constructed out of the response. It is
pointed out thereby that the electric susceptibility is generally expressed as
a ratio of the Hall conductance to the Landau gap.
