Skip to main content
SpringerLink
Log in

On abelian solutions to the Yang-Mills-Higgs equations

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

Abstract

The topology of some reducible connections in the (first) Georgi-Glashow model is considered. It is shown that pairs of U(1) connections with non-null Hopf index are minima of the Euclidean action under severe symmetry restrictions. Their physical meaning and some generalizations are outlined.

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. Donaldson, S., J. Diff. Geom. 18, 269 (1983).

    Google Scholar 

  2. VanBaal, P., Commun. Math. Phys. 94, 397 (1984); Braam, P., ‘Space-Time Symmetries in Gauge Theories’, Utrecht University.

    Google Scholar 

  3. Freed, D. and Uhlenbeck, K., Instantons and Four-Manifold, Springer-Verlag, New York, 1984.

    Google Scholar 

  4. Mandelstam, S., Phys. Rep. 23C, 245 (1976); 't Hooft, G., Nucl. Phys. B153, 141 (1979).

    Article  Google Scholar 

  5. Duff, M. and Madore, J., Phys. Rev. D18, 2788 (1978).

    Article  Google Scholar 

  6. Eguchi, T., Gilkey, P., and Hanson, A., Phys. Rep. 66C, 215 (1980).

    Article  Google Scholar 

  7. Georgi, H. and Glashow, S., Phys. Rev. Lett. 28, 1494 (1972).

    Article  Google Scholar 

  8. Nielsen, H. and Olesen, P., Nucl. Phys. B61, 45 (1973); Nambu, Y., Phys. Rev. D10, 4212 (1974).

    Article  Google Scholar 

  9. Chan, Hong-Mo and Tson, Sheung-Tsun, Nucl. Phys. B189, 364 (1981).

    Article  Google Scholar 

  10. Taubes, C., Commun. Math. Phys. 86, 257 (1982); 97, 473 (1985).

    Google Scholar 

  11. DeVega, H., Phys. Rev. D18, 2945 (1978); Wilczek, F., Phys. Rev. Lett. 51, 2250 (1983).

    Article  Google Scholar 

  12. Husemoller, D., Fiber Bundles, Springer-Verlag, New York, 1966, p. 199.

    Google Scholar 

  13. Jaffe, A. and Taubes, C., Vortices and Monopoles, Birkhaüser, Basle, 1980.

    Google Scholar 

  14. Bourguignon, J. and Lawson, H., Commun. Math. Phys. 79, 189 (1981); Chaohao, Gu, Phys. Rep. 80C, 251 (1980).

    Google Scholar 

  15. Hasenfratz, P. and 't Hooft, G., Phys. Rev. Lett. 36, 1110 (1976); Jackiw, R. and Rebbi, C., Phys. Rev. Lett. 36, 1116 (1976); Wilczek, F., Phys. Rev. Lett. 48, 1144 (1982).

    Article  Google Scholar 

  16. Atiyah, M., Hitchin, N., and Singer, I., Proc. Roy Soc. Lond. A362, 425 (1978); Atiyah, M., ‘The Geometry of Yang-Mills Fields’, Lezioni Fermiani, Scuola Normale Pisa, 1978.

    Google Scholar 

  17. Cerveró, J. and Mateos, J., Phys. Rev. Lett. 50, 1889 (1983).

    Article  Google Scholar 

  18. Bogomolny, E., Sov. J. Nucl. Phys. 24, 449 (1977).

    Google Scholar 

  19. Hitchin, N., Private letter.

  20. Atiyah, M., ‘The Moment Map in Symplectic Geometry’, in T.Willmore and N.Hitchin (eds.), Global Riemannian Geometry, Ellis Horwood, Chichester, 1984.

    Google Scholar 

  21. Rubakov, V., Nucl. Phys. B203, 311 (1982); Gómez, C., Lett. Matt. Phys. 8, 367 (1984).

    Article  Google Scholar 

  22. 't Hooft, G., Nucl. Phys. B190 [FS3], 455 (1981).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theoretical Physics Department, Salamanca University, 37008, Salamanca, Spain

    Juan Mateos Guilarte

Authors
  1. Juan Mateos Guilarte
    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

Guilarte, J.M. On abelian solutions to the Yang-Mills-Higgs equations. Lett Math Phys 12, 21–29 (1986). https://doi.org/10.1007/BF00400300

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00400300

Keywords

Search

Navigation