Skip to main content
SpringerLink
Log in

Planar diagrams

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We investigate the planar approximation to field theory through the limit of a large internal symmetry group. This yields an alternative and powerful method to count planar diagrams. Results are presented for cubic and quartic vertices, some of which appear to be new. Quantum mechanics treated in this approximation is shown to be equivalent to a free Fermi gas system.

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. 't Hooft, G.: Nucl. Phys. B72, 461–473 (1974)

    Google Scholar 

  2. 't Hooft, G.: Nucl. Phys. B75, 461–470 (1974)

    Google Scholar 

  3. Tutte, W. T.: Can. J. Math.14, 21–38 (1962)

    Google Scholar 

  4. Koplik, J., Neveu, A., Nussinov, S.: Nucl. Phys. B123, 109–131 (1977)

    Google Scholar 

  5. Mehta, M. L.: Random matrices. New-York and London: Academic Press 1967

    Google Scholar 

  6. Hioe, F. T., Montroll, E. W.: J. Math. Phys.16, 1945–1955 (1975)

    Google Scholar 

  7. 't Hooft, G.: Private communication

Download references

Author information

Authors and Affiliations

  1. Service de Physique Théorique, Centre d'Études Nucléaires de Saclay, F-91190, Gif-sur-Yvette, France

    E. Brézin, C. Itzykson, G. Parisi & J. B. Zuber

Authors
  1. E. Brézin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Itzykson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Parisi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. B. Zuber
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by R. Stora

ENS, Paris. On leave of absence from INFN-Frascati

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brézin, E., Itzykson, C., Parisi, G. et al. Planar diagrams. Commun.Math. Phys. 59, 35–51 (1978). https://doi.org/10.1007/BF01614153

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01614153

Keywords

Search

Navigation