The relation between Pauli and γ representation in QED3 and induced Chern-Simons term

Abstract

In this letter, we propose to introduce a new Abelian gauge field B μ corresponding to the so-called β symmetry into the normal Quantum Electrodynamics in 2+1 dimensions (QED 3 ) of γ representation. The resulting theory is shown to be equivalent to QED 3 containing two flavors of two-component fermions with mass of an opposite sign. We also show that B μ field can generate a ChernSimons term in perturbation theory. A comparison is made between the induced Chern-Simons term in the γ representation and that in Pauli representation.