Induced quantum numbers in (2+1)-dimensional QED

In this paper the vacuum-polarization effects of fermions interacting with Abelian gauge fields are studied in 2+1 dimensions. We find that for a gauge-field configuration with magnetic flux 2πF, there is an induced charge Q, spin S, and angular momentum J given by Q=-1/2(m/‖m‖)F, S=F/4, J=-(1/4)(m/‖m‖)$F^2$ (m=fermion mass). A simple argument is offered to explain the physics of these quantum numbers. Some subtleties associated with the induced spin and angular momentum are explained in detail. The induced spin is shown to be related to the (1+1)-dimensional chiral anomaly.