Skip to main content
SpringerLink
Log in

Reconstruction of the spontaneously broken gauge theory in non-commutative geometry

  • Published:
Il Nuovo Cimento A (1965-1970)

Summary

The scheme previously proposed by the present authors is modified to incorporate the strong interaction by affording the direct product internal symmetry. We do not need to prepare the extra discrete space for the colour gauge group responsible for the strong interaction to reconstruct the standard model and the left-right symmetric gauge model (LRSM). The approach based on non-commutative geometry leads us to present many attractive points such as the unified picture of the gauge and Higgs field as the generalized connection on the discrete spaceM 4×Z N. This approach leads us to unified picture of gauge and Higgs fields as the generalized connection. The standard model needsN=2 discrete space for reconstruction in this formalism. LRSM is still alive as a model with the intermediate symmetry of the spontaneously brokenSO(10) grand unified theory (GUT).N=3 discrete space is needed for the reconstruction of LRSM to include two Higgs bosonsφ andξ which are as usual transformed as (2, 2*, 0) and (1, 3, −2) underSU(2)L×SU(2)R×U(1)Y, respectively.ξ is responsible to makeν R Majorana fermion and so well explains the seesaw mechanism. Up and down quarks have different masses through the vacuum expectation value ofφ.

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. Connes A., inThe Interface of Mathematics and Particle Physics, edited byD. G. Quillen, G. B. Segal andS. T. Tsou (Clarendon Press, Oxford) 1990, p. 9. See also,Connes A. andLott J.,Nucl. Phys. B (Proc. Suppl.),18 (1990) 57.

    Google Scholar 

  2. Chamseddine A. H., Felder G. andFrölich J.,Phys. Lett. B,296 (1992) 109;Nucl. Phys. B,395 (1993) 672;Chamseddine A. H. andFrÖlich J.,Phys. Rev. D,50 (1994) 2823;Kastler D.,Rev. Math. Phys.,5 (1993) 477;Dubois-Violette M.,Class. Quantum Grav.,6 (1989) 1709;Coquereaux R., Esposito-Farese G. andVaillant G.,Nucl. Phys. B,353 (1991) 689;Dubois-Violette M., Kerner R. andMadore J.,J. Math. Phys.,31 (1990) 316;Balakrishna B., Gürsey F. andWali K. C.,Phys. Lett. B,254 (1991) 430;Phys. Rev. D,46 (1992) 6498;Coquereaux R., Esposito-Farese G. andScheck F.,Int. J. Mod. Phys. A,7 (1992) 6555;Coquereaux R., Haussling R., Papadopoulos N. andScheck F.,Int. J. Mod. Phys. A,7 (1992) 2809.

    Article  MathSciNet  ADS  Google Scholar 

  3. Sitarz A.,Phys. Lett. B,308 (1993) 311;J. Geom. Phys.,15 (1995) 123.

    Article  MathSciNet  ADS  Google Scholar 

  4. Ding H-G., Gou H-Y., Li J-M. andWu K.,Z. Phys. C,64 (1994) 123.

    Article  Google Scholar 

  5. Chen B. andWu K.,Z 2 ⊙Z 2 Discrete Symmetry in the Left-Right Symmetric Model SU(2)L×SU(2)R×U(1)B-L, preprint AS-ITP-93-64.

  6. Morita K. andOkumura Y.,Phys. Rev. D,50 (1994) 1016;Okumura Y.,Prog. Theor. Phys.,92 (1994) 625.

    Article  MathSciNet  ADS  Google Scholar 

  7. Morita K. andOkumura Y.,Prog. Theor. Phys.,91 (1994) 975;Okumura Y.,Phys. Rev. D,50 (1994) 1026.

    Article  MathSciNet  ADS  Google Scholar 

  8. Morita K. andOkumura Y.,Prog. Theor. Phys.,91 (1994) 959.

    Article  MathSciNet  ADS  Google Scholar 

  9. Naka S. andUmezawa E.,Prog. Theor. Phys.,92 (1994) 189.

    Article  MathSciNet  ADS  Google Scholar 

  10. Berry M. V.,Proc. R. Soc. London, Ser. A,392 (1984) 45.

    Article  ADS  Google Scholar 

  11. Okumura Y.,Prog. Theor. Phys.,94 (1995) 607.

    Article  MathSciNet  ADS  Google Scholar 

  12. Gell-Mann M., Ramond P. andSlanski R., inProceedings of the Workshop on Supergravity, Stony Brook, New-York, 1979, edited byP. van Nieuwenhuizen andD. Freedman (North-Holland, Amsterdam) 1980;Yanagida T., inProceedings of the Workshop on Unified Theories and Baryon Number in the Universe, Tsukuba, Japan, 1979, edited byA. Sawada andA. Sugamoto (KEK Report No.79-18 Tsukuba) 1979;Mohapartra R. N. andSenjanovic G.,Phys. Rev. Lett.,44 (1980) 912 and the references inFukugita M. andYanagida T.,Physics of neutrinos, inPhysics and Astrophysics of Neutrinos, edited byM. Fukugita andA. Suzuki (Springer-Verlag, Tokyo) 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Natural Science, Chubu University, 487, Kasugai, Japan

    Y. Okumura

  2. Department of Physics, Nagoya University, 464-01, Nagoya, Japan

    K. Morita

Authors
  1. Y. Okumura
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Morita
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. Okumura.

Additional information

The authors of this paper have agreed to not receive the proofs for correction.

This work was completed while YO stayed at University of Alberta.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Okumura, Y., Morita, K. Reconstruction of the spontaneously broken gauge theory in non-commutative geometry. Nuov Cim A 109, 311–326 (1996). https://doi.org/10.1007/BF02731017

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02731017

PACS

PACS

PACS

Search

Navigation