Nonrelativistic Quantum Electrodynamics: Leading Radiative Corrections

An effective field theory is constructed to describe low-energy processes in quantum electrodynamics—nonrelativistic quantum electrodynamics (NRQED). It is shown how the NRQED formalism makes it possible to develop a rigorous perturbation theory for calculating higher-order corrections in parameters $$~{v \mathord{\left/ {\vphantom {v c}} \right. \kern-0em} c}\sim Z\alpha $$ , $$\beta = {m \mathord{\left/ {\vphantom {m M}} \right. \kern-0em} M}$$ , where $$v$$ is the speed of electrons (muons) in atoms, and $${m \mathord{\left/ {\vphantom {m M}} \right. \kern-0em} M}$$ is the ratio of masses of light particles to those of heavy ones in a molecular system. As an example, the leading radiation correction of order $$m\alpha {{(Z\alpha )}^{4}}$$ is calculated. It is shown how the regularization parameter introduced into NRQED cancels in the final expression for the energy without leading to meaningless infinite results.