Three-dimensional quantum electrodynamics as an effective interaction

TL;DR

This paper derives a 2+1 dimensional quantum electrodynamics model from a 3+1 dimensional one using dimensional reduction, revealing a phase-dependent Chern--Simons term relevant for solid-state physics.

Contribution

It introduces a novel dimensional reduction approach to QED, producing a realistic 2+1D model with a unique phase structure and phase-dependent topological term.

Findings

Effective action shows interesting phase structure

Chern--Simons term survives only in the broken phase

Model applicable to solid-state systems

Abstract

We obtain a Quantum Electrodynamics in 2+1 dimensions by applying a Kaluza--Klein type method of dimensional reduction to Quantum Electrodynamics in 3+1 dimensions rendering the model more realistic to application in solid-state systems, invariant under translations in one direction. We show that the model obtained leads to an effective action exhibiting an interesting phase structure and that the generated Chern--Simons term survives only in the broken phase.