Skip to main content
SpringerLink
Log in

On Gell-Mann's λ-matrices,d- andf-tensors, octets, and parametrizations ofS U (3)

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

Abstract

The algebra ofS U (3) is developed on the basis of the matrices λ i ofGell-Mann, and identities involving the tensorsd i j k andf i j k occurring in their multiplication law are derived. Octets and the tensor analysis of the adjoint groupS U (3)/Z(3) ofS U (3) are discussed. Various explicit parametrizations ofS U (3) are presented as generalizations of familiarS U (2) results.

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. Gell-Mann, M.: The Eightfold way. California Institute of Technology Report CTSL-20 (1961), unpublished; reproduced in: The Eightfold Way,M. Gell-Mann andY. Ne'eman. New York: Benjamin Inc. 1964.

  2. Cutkosky, R. E., andP. Tarjanne: Phys. Rev.132, 1354 (1963);

    Google Scholar 

  3. Dullemond, C.: Ann. Phys.33, 214 (1965)

    Google Scholar 

  4. Kaplan, L. M., andM. Resnikoff: J. Math. Phys.8, 2194 (1967)

    Google Scholar 

  5. Levy, M.: Nuovo Cimento52, 23 (1967)

    Google Scholar 

  6. Mitter, P. K., andL. J. Swank: Preprint (1968)

  7. Michel, L., andL. A. Radicati: Preprint (1968)

  8. Macfarlane, A. J., andP. H. Weisz: Nuovo Cim.55A, 853 (1968), Preprint (1968).

    Google Scholar 

  9. Tarjanne, P.: Ann. Acad. Sci. Fenn. Ser. A. VI Physica, No. 105, (1962).

  10. Okubo, S.: Prog. Theoret. Phys. (Kyoto)27, 949 (1962).

    Google Scholar 

  11. Chang, P., andF. Gürsey: Phys. Rev.164, 1752 (1967).

    Google Scholar 

  12. Racah, G.: Lectures on group theory and spectroscopy. Princeton: University Press 1951, reprinted as CERN 61-8, 1961.

    Google Scholar 

  13. Okubo, S.: Phys. Letters8, 362 (1963)

    Google Scholar 

  14. Okubo, S.: Lectures on unitary symmetry, University of Rochester report, 1964, p. 83 and p. 170.

  15. Dalitz, R. H.: Proc. Intern. School of Physics Enrico Fermi, Course 32, p. 206, 1964. New York: Academic Press 1966.

    Google Scholar 

  16. Ademollo, M., andR. Gatto: Phys. Rev. Letters (1964).

  17. Zakharov, V. I., andI. Yu. Kobzarev: Sov. J. Nucl. Phys.1, 749 (1965).

    Google Scholar 

  18. Macfarlane, A. J.: Commun. math. Phys.

  19. Mukunda, N., andL. K. Pandit: J. Math. Phys.6, 746 (1965).

    Google Scholar 

  20. Littlewood, D. E.: University Algebra, p. 188. London: Heinemann 1958.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK

    A. J. Macfarlane, A. Sudbery & P. H. Weisz

Authors
  1. A. J. Macfarlane
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Sudbery
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. H. Weisz
    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

Macfarlane, A.J., Sudbery, A. & Weisz, P.H. On Gell-Mann's λ-matrices,d- andf-tensors, octets, and parametrizations ofS U (3). Commun.Math. Phys. 11, 77–90 (1968). https://doi.org/10.1007/BF01654302

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01654302

Keywords

Search

Navigation