Low Energy Description of Fermion Pairs in Topologically Massive QED$_{2+1}$ with $N$ Flavours

TL;DR

This paper derives a low-energy effective theory for fermion pairs in topologically massive QED$_{2+1}$ with multiple flavors, revealing their bosonic nature and impact on gauge field mass generation.

Contribution

It introduces a novel effective action describing fermion pairs as spin-1 bosons and explores their condensation effects in topologically massive QED$_{2+1}$.

Findings

Fermion pairs behave like doubly charged spin-1 bosons.

Condensation of pairs gives the gauge field a longitudinal mass.

An approximate SU(2) symmetry is discussed.

Abstract

In topologically massive QED$_{2+1}$ with $N$ flavours, there is the possibility that two equal-charged fermions can form a bound state pair in either s-wave or p-wave. We are concerned about the s-wave pairs and obtain the low energy effective action describing them. It is shown that the fermion pairs behave like doubly charged spin-1 bosons and, when they condense, the gauge field aquires the longitudinal mass. The approximate $SU(2)$ symmetry due to the similarity between the fermion pairs and the gauge field is discussed.