Skip to main content
SpringerLink
Log in

Luttinger Revisited—The Renormalization Group Approach

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Luttinger's contributions abound in different parts of many-body physics. Here I review the ones that appear when one uses the Renormalization Group (RG) to study the subject: the Luttinger Liquid, Luttinger's Theorem (on the volume of the Fermi surface) and the Kohn–Luttinger Theorem on the superconducting instability of all metals as one approaches absolute zero.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. F. D. M. Haldane, J. Phys. C 14:2585 (1981).

    Google Scholar 

  2. J. M. Luttinger, J. Math. Phys. 4:1154 (1963).

    Google Scholar 

  3. D. Mattis and E. H. Lieb, J. Math. Phys. 6:304 (1965).

    Google Scholar 

  4. R. Shankar, Physica A 177:530 (1991).

    Google Scholar 

  5. R. Shankar, Rev. Mod. Phys. 66:129 (1994).

    Google Scholar 

  6. G. Benfatto and G. Gallavotti, Phys. Rev. B 42:9967 (1990). Since their early work rigorous proofs of the results that were alluded to in the text, such as the nature of the occupation number at the Fermi surface, have been derived in G. Benfatto, G. Gallavitti, A. Procacci, and B. Scoppola, Comm. Math. Phys. 160:93 (1994), and F. Bonetto and V. Mastropietro, Comm. Math. Phys. 172:57 (1995).

    Google Scholar 

  7. J. Feldman and E. Trubowitz, Helv. Phys. Acta 63:157 (1990).

    Google Scholar 

  8. J. Polchinski, 1992, Effective Field Theory and the Fermi Surface, preprint NSF-ITP-92-XX UTTG-20-92, printed in 1992 TASI proceedings.

  9. P. W. Anderson, in Basic Notions of Condensed matter Physics (Benjamin Publishers, 1984).

  10. J. M. Luttinger, Phys. Rev. 119:1153 (1960).

    Google Scholar 

  11. W. Kohn and J. M. Luttinger, Phys. Rev. 118:41 (1960).

    Google Scholar 

  12. J. M. Luttinger and J. Ward, Phys. Rev. 118:1417 (1960).

    Google Scholar 

  13. C. N. Yang and C. P. Yang, Phys. Rev. 150:321 (1976).

    Google Scholar 

  14. C. Di Castro, and W. Metzner, Phys. Rev. Lett. 67:3852 (1991).

    Google Scholar 

  15. J. Solyom, Adv. Phs. 28:201 (1979).

    Google Scholar 

  16. P. Morel and P. W. Anderson, Phys. Rev. 125:1263 (1962).

    Google Scholar 

  17. W. Kohn and J. M. Luttinger, Phys. Rev. Lett. 15:524 (1965).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sloane Laboratory of Physics, Yale University, New Haven, Connecticut, 06520

    R. Shankar

Authors
  1. R. Shankar
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shankar, R. Luttinger Revisited—The Renormalization Group Approach. Journal of Statistical Physics 103, 485–502 (2001). https://doi.org/10.1023/A:1010333114332

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010333114332

Search

Navigation