Coulomb Gauge Quantization and Renormalization of the Chern–Simons Theory Coupled to Fermions

Abstract

We study the quantization and the one-loop renormalization of the model resulting from the coupling of charged fermions with a Chern–Simons field, in the Coulomb gauge. A proof of the Lorentz covariance of the physical quantities follows after establishing the Dirac–Schwinger algebra for the Poincaré densities and the transformation properties of the fields under the Poincaré group. The Coulomb gauge one-loop renormalization program is, afterwards, implemented. The noncovariant form of the one-loop fermion propagator, Chern–Simons field propagator and the vertex are explicitly obtained. Finally, the electron anomalous magnetic moment is calculated stressing that, due to the peculiarities of the Coulomb gauge, the contributions from the self-energy diagrams turn out to be essential.

Anomalous magnetic moment of electron in Chern–Simons QED

“…Asymptotically, as κ becomes large, they behave as This indeed agrees with the large M result in [11]. In fact, recalling that the pure Chern-Simons theory can be obtained from the Maxwell-Chern-Simons theory in the limit e, M → ∞, such that e 2 M is fixed, we obtain the well-known result [11,12] that…”

“…Subsequently, this result has also been derived from a calculation in the pure Chern-Simons theory in the Coulomb gauge [12]. Our study, on the other hand, represents a complete systematic analysis of the anomalous magnetic moment at one loop in Chern-Simons theories with and without the Maxwell term, both at zero as well as at finite temperature.…”

“…In Section 2, we analyze the question of the anomalous magnetic moment in the MCS theory at zero temperature for an arbitrary value of the Chern-Simons coefficient which brings out the problem of the infrared divergence. Taking the large M limit, we then obtain the known result for the pure CS theory [11,12]. In Section 3, we present our analysis of the finite temperature behavior of the anomalous magnetic moment.…”

Low energy limit of the Chern-Simons theory coupled to fermions

“…In section III we examine the relativistic model (1.1). After summarizing the renormalization program [6] we prove that radiative corrections induce both an "anomalous" magnetic term and a Maxwell term, absents in (1.2). To calculate the one loop corrections to the fermion-fermion scattering amplitudes we will employ a scheme which separates the contributions of the low and high momenta intermediary states [7].…”

Non relativistic limit of a Model of Fermions interacting through a Chern-Simons field

“…We can also see that the magnetic momenta of the spin plus and minus fermions are corrected to ( [7])…”