The renormalization-group approach for Fermi systems in the presence of singular forward scattering

Within the framework of perturbative renormalization group, we analyze the problem of spinless fermions either coupled to a transverse gauge field or interacting through a longitudinal singular potential, in generic spatial dimensions d. The model of fermions interacting through a singular potential due to the proximity to a phase-separation instability is also discussed. We show how to develop a unified renormalization-group treatment making use of the so-called "loop cancellation", coming from the peculiar symmetry properties of models with forward scattering. This allows to solve the renormalization-group equations and to compute the asymptotic properties of the single particle propagator, also providing exact scaling results. (C) 2001 Elsevier Science B.V. All rights reserved.