The Low Energy Limit of the Chern-Simons Theory Coupled to Fermions

TL;DR

This paper investigates the nonrelativistic limit of a quantum Chern-Simons theory coupled to fermions, revealing effective interactions and a method to connect relativistic and nonrelativistic quantum theories.

Contribution

It derives the nonrelativistic effective Lagrangian including vacuum polarization, magnetic moments, and induced fermionic interactions, and introduces a method to relate relativistic and nonrelativistic theories.

Findings

Identification of vacuum polarization effects in the nonrelativistic limit.

Discovery of an induced quartic fermionic interaction.

A method to separate low and high loop momenta in quantum calculations.

Abstract

We study the nonrelativistic limit of the theory of a quantum Chern--Simons field minimally coupled to Dirac fermions. To get the nonrelativistic effective Lagrangian one has to incorporate vacuum polarization and anomalous magnetic moment effects. Besides that, an unsuspected quartic fermionic interaction may also be induced. As a by product, the method we use to calculate loop diagrams, separating low and high loop momenta contributions, allows to identify how a quantum nonrelativistic theory nests in a relativistic one.