Skip to main content
SpringerLink
Log in

A model of gauge fields as Cartan connection and related matter fields

  • Published:
Il Nuovo Cimento A (1971-1996)

Summary

Quantum gauge theory based on a concept of a fiber bundle with Cartan connection is investigated. We study gravity as a prototype and get some interesting results, among which it is found that the symmetric nature of the underlying fiber space induces the existences of FP-ghost, antighost, gauge-fixing, gaugeon and its pair field in a nonad hoc way. These results are generalized to other Yang-Mills theories. We also propose a model for fundamental elementary matter fields inspired by such gauge mechanism, which are a spin-1/2 and a spin-0 fields carrying the electric charge «e/6». Quarks, leptons, and usual weak bosons (W±, Z0) are composite objects of them.

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. S. Kobayashi:Ann. Math.,43, 119 (1957).

    Google Scholar 

  2. W. Drechsler:Lecture Notes in Physics,67, edited byJ. Ehlers et al. (Springer-Verlag, 1977), p. 145;J. Math. Phys.,18, 1358 (1977).

    Article  ADS  MathSciNet  Google Scholar 

  3. S. Kobayashi andK. Nomizu:Foundations of Differential Geometry (Wiley, New York, N.Y., 1963, Vol. I, 1969, Vol. II).

    MATH  Google Scholar 

  4. W. Drechsler:Ann. Inst. Henri Poincaré,37, 155 (1982);Fortschr. Phys.,32, 449 (1984);J. Math. Phys.,26, 41 (1985);W. Drechsler andW. Thacker:Class. Q. Grav.,4, 291 (1987).

    MathSciNet  Google Scholar 

  5. A. A. Tsyeytlin:Phys. Rev. D,26, 3327 (1983).

    Article  ADS  Google Scholar 

  6. A. Barut andR. Raczka:Theory of Group Representations and Applications (PWN-Polish Scientific Publishers, Warszawa, 1980), p. 123.

    MATH  Google Scholar 

  7. K. Nomizu:Am. J. Math.,76, 33 (1954).

    Article  MathSciNet  Google Scholar 

  8. S. Kobayashi:Differential Geometry of Connections and Gauge Theory, in Japanese (Shokabo, Tokyo, 1989), p. 63.

  9. L. Bonora andP. Cotta-Ramusino:Commun. Math. Phys.,87, 589 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  10. T. Kugo andI. Ojima:Phys. Lett. B,73, 459 (1978);Prog. Theor. Phys.,60, 1869 (1978).

    Article  ADS  Google Scholar 

  11. N. Nakanishi:Prog. Theor. Phys.,35, 1111 (1966);38, 881 (1967).

    Article  ADS  Google Scholar 

  12. K. Yokoyama:Prog. Theor. Phys.,51, 1956 (1974);K. Yokoyama, M. Takeda andM. Monda:Prog. Theor. Phys.,64, 1412 (1980).

    Article  ADS  Google Scholar 

  13. T. T. Wu andC. N. Yang:Phys. Rev. D,13, 3233 (1976);J. P. Hsu andM. D. Xin:Phys. Rev. D,24, 471 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  14. S. Coleman:Phys. Lett. B,70, 59 (1977);A. Trautman:J. Phys. A,13, L1 (1980);Acta Phys. Austr., Suppl.,23, 401 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  15. K. Nomizu:Introduction to Modern Differential Geometry, in Japanese (Shokabo, Tokyo, 1981), p. 171.

  16. H. Georgi andS. L. Glashow:Phys. Rev. Lett.,32, 438 (1974).

    Article  ADS  Google Scholar 

  17. Private communication to Dr. Tsujimaru.

  18. J. D. Bjorken:Phys. Rev. D,19, 335 (1979).

    Article  ADS  MathSciNet  Google Scholar 

  19. P. Q. Hung andJ. J. Sakurai:Nucl. Phys. B,143, 81 (1978).

    Article  ADS  Google Scholar 

  20. F. D. Stacey et al.:Rev. Mod. Phys.,59, 157 (1987).

    Article  ADS  Google Scholar 

  21. T. Matsushima: DPNU-89-30 (1989); DPNU-89-50 (1989).

  22. T. Matsushima: DPN-89-31 (1989).

  23. J. C. Pati andA. Salam:Nucl. Phys. B,214, 109 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  24. Y. Ohnuki:Unitary Representation of the Poincaré Group and Relativistic Wave Equations (World Scientific, Singapore, 1988).

    Book  MATH  Google Scholar 

  25. H. Harari andN. Seiberg:Phys. Lett. B,98, 269 (1981);Nucl. Phys. B,204, 141 (1982).

    Article  ADS  Google Scholar 

  26. D. Lüst, A. Masiero andM. Roncadelli:Phys. Rev. D,25, 3096 (1982);T. Yanagita andM. Yoshimura:Phys. Rev. Lett.,45, 71 (1980).

    Article  ADS  Google Scholar 

  27. S. Kobayashi:Can. J. Math.,8, 145 (1956).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Nagoya University, Chikusa-ku, 464-01, Nagoya, Japan

    T. Matsushima

Authors
  1. T. Matsushima
    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

Matsushima, T. A model of gauge fields as Cartan connection and related matter fields. Nuov Cim A 106, 139–162 (1993). https://doi.org/10.1007/BF02800058

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02800058

PACS 12.10.Gq

PACS 11.90

PACS 03.70

Search

Navigation