Skip to main content
SpringerLink
Log in

Quaternion Octonion Reformulation of Quantum Chromodynamics

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

We have made an attempt to develop the quaternionic formulation of Yang–Mill’s field equations and octonion reformulation of quantum chromo dynamics (QCD). Starting with the Lagrangian density, we have discussed the field equations of SU(2) and SU(3) gauge fields for both cases of global and local gauge symmetries. It has been shown that the three quaternion units explain the structure of Yang–Mill’s field while the seven octonion units provide the consistent structure of SU(3) C gauge symmetry of quantum chromo dynamics.

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. Dickson, L.E.: Ann. Math. 20, 155 (1919)

    Article  MATH  Google Scholar 

  2. Hamilton, W.R.: Elements of Quaternions. Chelsea, New York (1969)

    Google Scholar 

  3. Tait, P.G.: An Elementary Treatise on Quaternions. Oxford University Press, London (1875)

    Google Scholar 

  4. Cayley, A.: Philos. Mag. 26, 208 (1845)

    Google Scholar 

  5. Graves, R.P.: Life of Sir William Rowan Hamilton. Arno Press, New York (1975). 3 volumes

    Google Scholar 

  6. Baez, J.C.: Bull. Am. Math. Soc. 39, 145 (2001)

    Article  MathSciNet  Google Scholar 

  7. Günaydin, M., Gürsey, F.: J. Math. Phys. 14, 1651 (1973)

    Article  MATH  Google Scholar 

  8. Günaydin, M., Gürsey, F.: Phys. Rev. D 9, 3387 (1974)

    Article  ADS  Google Scholar 

  9. Domokos, G., Domokos-Kovesi, S.: Phys. Rev. D 19, 2984 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  10. Morita, K.: Prog. Theor. Phys. 65, 787 (1981)

    Article  ADS  Google Scholar 

  11. Morita, K.: Prog. Theor. Phys. 73, 999 (1985)

    Article  MATH  ADS  Google Scholar 

  12. Morita, K.: Prog. Theor. Phys. 65, 2071 (1981)

    Article  MATH  ADS  Google Scholar 

  13. Morita, K.: Prog. Theor. Phys. 67, 1860 (1982)

    Article  ADS  Google Scholar 

  14. Morita, K.: Prog. Theor. Phys. 66, 1519 (1981)

    Article  MATH  ADS  Google Scholar 

  15. Griffiths, D.: Introduction to Elementary Particles. Wiley, New York (1987)

    Book  Google Scholar 

  16. Rawat, S., Negi, O.P.S.: Int. J. Theor. Phys. 48, 2222 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  17. Negi, O.P.S.: Higher dimensional supersymmetry. Talk presented at conference on “Function Theories in Higher Dimensions”, Tampere Univ. of Technology, Tampere, Finland, 12–16 June 2006. arXiv:hep-th/0608019

  18. Bisht, P.S., Pandey, B., Negi, O.P.S.: Fizika B (Zagreb) 17, 405 (2008)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Kumaun University, S.S.J. Campus, Almora, 263601, Uttarakhand, India

    Pushpa, P. S. Bisht & O. P. S. Negi

  2. Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing, 100080, P.R. China

    Tianjun Li

Authors
  1. Pushpa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. S. Bisht
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tianjun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. O. P. S. Negi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. P. S. Negi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pushpa, Bisht, P.S., Li, T. et al. Quaternion Octonion Reformulation of Quantum Chromodynamics. Int J Theor Phys 50, 594–606 (2011). https://doi.org/10.1007/s10773-010-0579-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-010-0579-8

Keywords

Search

Navigation