Effective Theory for Parity Conserving $QED_3$

TL;DR

This paper develops an effective higher derivative theory for a 3D Abelian gauge field, derived by integrating out heavy matter, and computes the one-loop effective action for constant magnetic fields.

Contribution

It introduces a novel higher derivative effective theory for parity-conserving QED in three dimensions and explicitly evaluates the one-loop effective action for constant magnetic fields.

Findings

Explicit form of the one-loop effective action for constant magnetic fields.

Derivation of a higher derivative effective theory from integrating out heavy matter.

Quantization of the gauge field within this effective framework.

Abstract

We consider a higher derivative effective theory for an Abelian gauge field in three dimensions, which represents the result of integrating out heavy matter fields interacting with a classical gauge field in a parity-conserving way. We retain terms containing up to two derivatives of $F_{\mu\nu}$, but make no assumption about the strength of this field. We then quantize the gauge field, and compute the one-loop effective action for a constant $\fmn$. The result is explicitly evaluated for the case of a constant magnetic field.