  The electrons in undoped graphene behave as massless Dirac fermions.
Therefore graphene can serve as an unique condensed-matter laboratory for the
study of various relativistic effects, including quantum electrodynamics (QED)
phenomena. Although theoretical models describing electronic properties of
graphene have been elaborated in details, the QED effects were usually
neglected. In this paper we demonstrate theoretically that QED can drastically
modify electronic properties of graphene. We predict the following QED effect -
the opening of the band gap in a graphene monolayer placed inside a planar
microcavity filled with an optically active media. We show that this phenomenon
occurs due to the vacuum fluctuations of the electromagnetic field and is
similar to such a well-known phenomenon as a vacuum-induced splitting of atomic
levels (the Lamb shift). We estimate the characteristic value of the band gap
and find that it can sufficiently exceed the value of the Lamb shift.
