Physical origin of topological mass in 2 + 1 dimensions

In this paper QED in 2 + 1 dimensions is studied. We offer a simple physical description of the mechanism that gives rise to anomalous fermion currents and the “topological” mass (Chern-Simons term) in the effective gauge theory. The dynamical properties of the fermions are analyzed and explained in some detail. The physical properties responsible for these anomalous effects are identified and the mechanisms clarified. A novel result that follows from our discussion is that the ground state carries spin (S) as well as charge (Q) and that S = 12(m/|m|)Q. The relation of these effects to the 1 + 1-dimensional chiral anomaly and to some other topological features is discussed. The possible connection between QED in 2 + 1 dimensions and theories of the quantum Hall effect is briefly studied. Even though both theories contain crossed-field currents, a detailed analysis of the structure of QED shows that they are different even at a physical level. Hence QED in 2 + 1 is not a suitable model for the quantum Hall effect.