Classical solutions of Maxwell's equations in (2+1)-dimensional electrodynamics with the Chern-Simons term

Maxwell's equations associated with (2+1)-dimensional electrodynamics plus a Chern-Simons term are solved for the electromagnetic potentials Aμ(r) using matrix methods originally proposed by Moses [Phys. Rev. 113, 1670 (1959)] for 3+1 dimensions. Static as well as time-dependent solutions in the presence of sources are obtained. Additionally, for the former, closed-form expressions, which agree with the asymptotic (r→) limit for Aμ(r) in the literature, are worked out easily. Using these results for static potentials, a qualitative discussion of the relativistic hydrogen atom in 2+1 dimensions is presented. It is shown that the Klein paradox, which preempts the possibility of bound-state solutions with the usual logarithmically increasing Coulomb potential in 2+1 dimensions, is easily evaded with the presence of the Chern-Simons term. Attempts to formulate a quantitative approach to the problem are briefly discussed. © 1989 The American Physical Society.