The effect of charged fermion pair production hy a strong external Coulomb field in two spatial dimensions is studied. Exact solutions to the Dirac equation have been found for a Coulomb field in 2+1 dimensions. It is shown that the behavior of the lower energy levels of an electron in a strong Coulomb field differs significantly in the cases of two and three spatial dimensions. An equation has been obtained for the critical charge and solved numerically for a simple model. The critical charge in 2+1 dimensions is much smaller than its value for the same model in 3+1 dimensions.
Department of Theoretical Physics, Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia