An Introduction to NRQED

TL;DR

This paper provides a comprehensive pedagogical overview of NRQED, an effective field theory for non-relativistic spin-half particles interacting with electromagnetic fields, including detailed Lagrangian construction and an application to Thomson scattering.

Contribution

It offers a detailed derivation of the NRQED Lagrangian up to order 1/M^2 and demonstrates its application to low-energy photon scattering.

Findings

Derived the NRQED Lagrangian up to order 1/M^2

Applied NRQED to calculate Thomson scattering cross section

Clarified the construction of effective field theories for composite particles

Abstract

We present a pedagogical introduction to NRQED (non-relativistic quantum electrodynamics). NRQED is an effective field theory that describes the interaction of non-relativistic, possibly composite, spin-half particle with the electromagnetic field. We explain in detail how the NRQED Lagrangian is constructed up to and including order $1/M^2$, where $M$ is the mass of the spin-half particle. As a sample application, we derive the Thomson scattering cross section for the low energy scattering of a photon and a possibly composite spin-half particle.