The electron propagator in external electromagnetic fields in low dimensions

Abstract

We study the electron propagator in quantum electrodynamics in one and two spatial dimensions in the presence of external electromagnetic fields. In this case, the propagator is not diagonal in momentum space. We obtain the propagator on the basis of the eigenfunctions of the operator (gamma center dot Pi)(2) in terms of which the propagator acquires a free form. Pi(mu) is the canonical momentum operator and gamma(mu) are the Dirac matrices. In two dimensions, we work with an irreducible representation of the Clifford algebra and consider to all orders the effects of an arbitrary magnetic field perpendicular to the plane of motion of the electrons. We then discuss the special cases of a uniform magnetic field and an exponentially damped static magnetic field. These cases are relevant to graphene in the massless limit. We further consider the electron propagator for the massive Schwinger model and incorporate the effects of a constant electric field to all orders. (C) 2010 American Association of Physics Teachers. [DOI: 10.1119/1.3311656]