Effective Field Theory for Short-Range Forces

Abstract

The method of effective field theories (EFTs) is developed for the scattering of two particles at wavelengths which are large compared to the range of their interaction. It is shown that the renormalized EFT is equivalent to the effective range expansion, to a Schroedinger equation with a pseudo-potential, and to an energy expansion of a generic boundary condition at the origin. The roles of regulators and potentials are also discussed. These ideas are exemplified in a toy model.