Introduction to effective field theory

The basic idea behind effective field theory (EFT) methods is to describe nature in terms of a fully consistent quantum field theory, but one which is valid in a limited energy range. Now strictly speaking this means that almost any theory is an EFT except string theories that try to be a theory of everything (TOE). Indeed even the quintessential quantum field theory—quantum electrodynamics—is an EFT in that it must break down at the very highest energies. In fact we represent the high energy contribution in terms of a conterterm which, together with the divergent component from the loop integration, we fit in terms of the experimental mass and charge. In order to get a better feel for this idea it is useful to consider a simpler example from the regime of ordinary quantum mechanics—that of Rayleigh scattering, or why the sky is blue.