  The Schwinger mechanism, the production of charged particle-antiparticle
pairs in a macroscopic external electric field, is derived for 2+1 dimensional
theories. The rate of pair production per unit area for four species of
massless fermions, with charge $q$, in a constant electric field $E$ is given
by $ \pi^{-2} \hbar^{-3/2} \tilde{c}^{-1/2} (q E)^{3/2} $ where $\tilde{c}$ is
the speed of light for the two-dimensional system. To the extent undoped
graphene behaves like the quantum field-theoretic vacuum for massless fermions
in 2+1 dimensions, the Schwinger mechanism should be testable experimentally. A
possible experimental configuration for this is proposed. Effects due to
deviations from this idealized picture of graphene are briefly considered. It
is argued that with present day samples of graphene, tests of the Schwinger
formula may be possible.
