Fermions in strong external fields in 2+1 and 1+1 dimensions

The creation of electron-positron pairs from a vacuum by an external Coulomb field is examined within (2+1)-dimensional quantum electrodynamics. If the electromagnetic coupling constant exceeds 0.62 (Z= 85), then in a simple model with a finite-size nucleus, the lower electron level crosses the boundary of the negative-energy continuum (i.e., Dirac sea), and a hole (i.e., positively charged fermion) appears in the negative-energy continuum. An equation is obtained that describes the levels of the ground and excited electron states in a strong Coulomb field of the nucleus. The critical nucleus charge is found for a few lowest electron states. The critical charge in 2+1 dimensions is significantly smaller than in 3+1 dimensions. The problem is reduced to the case of a bounded Coulomb field in 1+1 dimensions without a magnetic field. The interaction of a fermion and an external scalar field in 2+1 and 1+1 dimensions is investigated. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol 122, No. 3, pp. 372–384, March, 2000