Skip to main content
SpringerLink
Log in

Revisiting the role of octonions in hadronic physics

  • Physics of Elementary Particles and Atomic Nuclei. Theory
  • Published:
Physics of Particles and Nuclei Letters Aims and scope Submit manuscript

Abstract

Octonions and their split versions are shown to be applicable to the solutions of a large number of problems in hadronic physics, from the foundations of exceptional groups that are used in grand unified theories, to heterotic strings, to the non-Desarguesian geometric property of space-time symmetries, twistors, harmonic superspace, conformal field theories, etc. Upon a brief review of these investigations we proceed to show how they are used in the unification of ancient and modern geometries, which in turn open new avenues for, and goes far beyond in providing, geometric foundations for the existence of internal symmetries such as color and flavor.

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. A. Galperin, E. Ivanov, V. Ogievetsky, and E. Sokatchev, Ann. Phys. Rev. 185 (1988).

    Google Scholar 

  2. M. Evans, F. Gursey, and V. Ogievetsky, Phys. Rev. D 47, 3496 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  3. M. J. Duff, J. M. Evans, R. R. Khuri, J. X. Lu, and R. Minasian, Phys. Rev. B 412, 281 (1997).

    Google Scholar 

  4. P. Ramond, Phys. Rev. D: Part. Fields 3, 2415 (1971).

    Article  ADS  Google Scholar 

  5. A. Neveu and J. Schwarz, Nucl. Phys. B 31, 86 (1971).

  6. T. A. Golfand and E. P. Likhtman, JETP Lett. 13, 323 (1971).

  7. D. V. Volkov and V. P. Akulov, Phys. Lett. B 46, 109 (1973).

    Article  ADS  Google Scholar 

  8. J. Wess and B. Zumino, Nucl. Phys. B 70, 39 (1974), Phys. Lett. B 49, 52 (1974).

    Article  ADS  Google Scholar 

  9. A. de Rujula, H. Georgi, and S. L. Glashow, Phys. Rev. D: Part. Fields 12, 147 (1975).

    Article  ADS  Google Scholar 

  10. D. B. Lichtenberg, W. Namgung, E. Predazzi, and J. G. Wills, Phys. Lett. 48, 1653 (1982)

    Article  Google Scholar 

  11. W. Namgung and D. B. Lichtenberg, Lett. Nuovo Cim. 41, 597 (1984)

    Article  Google Scholar 

  12. A. Martin, Z. Phys. C 32, 359 (1986), Symmetry in Nature (Scuola Normale Superiore, Pisa,1989), Vol. 2, p. 523.

  13. M. Anselmino, E. Predazzi, S. Ekelin, S. Fredriksson, and D. B. Lichtenberg, Rev. Mod. Phys. 65, 1199 (1993).

    Article  ADS  Google Scholar 

  14. S. Catto and F. Gursey, Nuovo Cim. A 86, 201 (1985).

    Article  ADS  Google Scholar 

  15. T. Eguchi, Phys. Lett. B 59, 457 (1975).

    Article  ADS  Google Scholar 

  16. I. Bars and A. J. Hanson, Phys. Rev. D: Part. Fields 13, 1744 (1976).

    Article  ADS  Google Scholar 

  17. K. Johnson and C. B. Thorn, Phys. Rev. D: Part. Fields 13, 1934 (1976).

    Article  ADS  Google Scholar 

  18. S. Catto and F. Gürsey, Nuovo Cim. A 99, 685 (1988).

  19. S. Catto, Y. Gürcan, A. Khalfan, and L. Kurt, J. Phys. 670, 012016 (2016).

  20. M. Günaydin and F. Gürsey, J. Math. Phys. 14, 1651 (1973).

  21. S. Okubo, Introduction to Octonion and other Nonassociative Algebras in Physics, vol. 2 of Montroll Memorial Lecture Series in Mathematical Physics (Cambridge Univ. Press, Cambridge, 1995).

    Book  MATH  Google Scholar 

  22. J. Baez, Bull. Am. Math. Soc. 39, 145–205 (2002).

    Article  Google Scholar 

  23. S. Catto, “Exceptional projective geometries and internal symmetries,” arXiv:hep-th/0302079.

  24. P. S. Bisht, B. C. Chanyal, and O. S. Negi, Int. J. Theor. Phys. 49, 1333 (2010), Int. J. Theor. Phys. 50, 1919 (2011), Int. J. Theor. Phys. 51, 3410 (2012), Int. J. Theor. Phys. 52, 3522 (2013), Int. J. Theor. Phys. 54, 3532 (2015).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bogoluibov Laboratory of Theoretical Physics, JINR, Dubna, Moscow oblast, 141980, Russia

    C. Burdik

  2. Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Prague, CZ-120 00, Czech Republic

    C. Burdik

  3. Physics Department, The Graduate School, City University of New York, New York, NY, 10016-4309, USA

    S. Catto

  4. Theoretical Physics Group, Rockefeller University, New York, NY, 10021-6399, USA

    S. Catto

  5. Department of Science, Borough of Manhattan CC, LIC, NY, 10007, USA

    Y. Gürcan & L. Kurt

  6. Department of Natural Sciences, LaGuardia CC, The City University of New York, LIC, NY, 11101, USA

    A. Khalfan

Authors
  1. C. Burdik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Catto
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. Gürcan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Khalfan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. L. Kurt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Catto.

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Burdik, C., Catto, S., Gürcan, Y. et al. Revisiting the role of octonions in hadronic physics. Phys. Part. Nuclei Lett. 14, 390–394 (2017). https://doi.org/10.1134/S1547477117020042

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1547477117020042

Search

Navigation