1997/01/03 by Walter Metzner, W. Metzner, Metzner, W. +4
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Condensed Matter (cond-mat) #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum, superfluid, helium dynamics #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9701012
142 pages, LATEX, 28 postscript figures, to appear in Adv. Phys
arxiv created 1997/01/03 · openalex publication_date 1997/01/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We review the theory of interacting Fermi systems whose low-energy physics is governed 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 as the momentum distribution function, the single-particle propagator and low-energy response functions in each class. The renormalization group for Fermi systems will be reviewed and applied as a link between microscopic models and effective low-energy theories. Particular attention is payed to conservation laws, which constrain any effective low-energy theory of interacting Fermi systems. In scattering processes with small momentum transfers the velocity of each scattering particle is (almost) conserved. This asymptotic conservation law leads to non-trivial cancellations of Feynman diagrams and other simplifications, making thus possible a non-perturbative treatment of forward scattering via Ward identities or bosonization techniques.