Chern-Simons Spinor Electrodynamics in the Light-Cone Gauge

TL;DR

This paper investigates one-loop quantum corrections in Chern-Simons spinor electrodynamics within the light-cone gauge, demonstrating gauge invariance and reproducing known quantum effects using a hybrid regularization approach.

Contribution

It provides a detailed calculation of quantum corrections in light-cone gauge and confirms gauge invariance of the effective action, extending previous covariant gauge results.

Findings

Quantum corrections reproduce parity-even Maxwell term and anomalous magnetic moment.

Ward identities are explicitly verified in the light-cone gauge.

The local quantum effective action remains gauge invariant in the light-cone gauge.

Abstract

The one-loop quantum corrections of Chern-Simons spinor electrodynamics in the light-cone gauge has been investigated. We have calculated the vacuum polarization tensor, fermionic self-energy and on-shell vertex correction with a hybrid regularization consisting of a higher covariant derivative regularization and dimensional continuation. The Mandelstam-Leibbrandt prescription is used to handle the spurious light-cone singularity in the gauge field propagator. We then perform the finite renormalization to define the quantum theory. The generation of the parity-even Maxwell term and the arising of anomalous magnetic moment from quantum corrections are reproduced as in the case of a covariant gauge choice. The Ward identities in the light-cone gauge are verified to satisfy explicitly. Further, we have found the light-cone vector dependent sector of local quantum effective action for the fermion is explicitly gauge invariant, and hence the covariance of $S$-matrix elements of the theory can be achieved.