Fermi systems with strong forward scattering

Abstract

We review the theory of interacting Fermi systems whose low-energy physics is dominated by forward scattering, i.e. scattering processes generated by effective interactions with small momentum transfers. These systems include Fermi liquids as well as several important non-Fermi liquid phases: one-dimensional Luttinger liquids, systems with long-range interactions, and fermions coupled to a gauge field. We report results for the critical dimensions separating different "universality classes", and discuss the behavior of physical quantities such as the momentum distribution function, the single-particle propagator and low-energy response functions in each class.