QED in Two Spatial Dimensions

Abstract

We briefly discuss general, though unfamiliar, aspects of 2+1-dimensional QED including a Chern-Simons term, distinguishing between a one-fermion (irreducible) and a two-fermion (reducible) formulation of the theory; each formulation exhibits different symmetry properties with respect to, for example, parity or chiral symmetry. The quantum aspects of these symmetries are investigated in detail to the one-loop level; we describe, as examples, the formation of a magnetically induced chiral condensate in the parity-preserving reducible formulation, and the perturbative generation of a parity-odd Chern-Simons term in the irreducible formulation. The relation between symmetry-breaking patterns and fermionic zero modes is outlined.