Fermion pair creation by a strong Coulomb field in 2+1 dimensions

The creation of charged fermion pairs by a strong external Coulomb field in a space with two dimensions is investigated. Exact solutions to the Dirac equation are found for the Coulomb external field in 2+1 dimensions. The equation for determining the critical charge is obtained and is numerically solved for a simplified model. The critical charge for 2+1 dimensions is much less than the critical charge for the similar model with 3+1 dimensions. The influence of the vacuum polarization on the critical charge is studied in the one-loop approximation to the (2+1)-dimensional quantum electrodynamics. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 116, No. 2, pp. 277–287, August, 1998.