  The virtues of an effective field theory (EFT) approach to many-body problems
are illustrated by deriving the expansion for the energy of an homogeneous,
interacting Fermi gas at low density and zero temperature. A renormalization
scheme based on dimensional regularization with minimal subtraction leads to a
more transparent power-counting procedure and diagrammatic expansion than
conventional many-body approaches. Coefficients of terms in the expansion with
logarithms of the Fermi momentum are determined by the renormalization
properties of the EFT that describes few-body scattering. Lessons for an EFT
treatment of nuclear matter are discussed.
