Skip to main content
Log in

Charged states in ℤ2 gauge theories

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

Abstract

Charged translation covariant states with finite energy are constructed in the Higgs phase of the ℤ2 gauge theory coupled to a ℤ2 matter field.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Wilson, K.: Confinement of quarks. Phys. Rev. D10, 2445 (1974)

    Google Scholar 

  2. Seiler, E.: Gauge theories as a problem of constructive quantum field theory and statistical mechanics. In: Lecture Notes in Physics, Vol. 159. Berlin, Heidelberg, New York: Springer 1982

    Google Scholar 

  3. Mack, G., Meyer, H.: A disorder parameter that tests for confinement in gauge theories with quark fields. Nucl. Phys.200B, 249 (1982)

    Google Scholar 

  4. Bricmont, J., Fröhlich, J.: An order parameter distinguishing between different phases of Lattice gauge theories with matter fields. Phys. Lett.122B, 73–77 (1983)

    Google Scholar 

  5. Fredenhagen, K.: Structural aspects of gauge theories in the algebraic framework of quantum field theories, (Talk presented at the Colloquium in honour of Prof. R. Haag at the occasion of his 60th birthday, Hamburg, November 15, 1982), University Freiburg, THEP 82/9

  6. Wegner, F.: Duality in generalized Ising models and phase transitions without local order parameters. J. Math. Phys.12, 2259 (1971)

    Google Scholar 

  7. Gallavotti, G., Guerra, F., Miracle-Solé, S.: Mathematical problems in theoretical physics, In: Lecture Notes in Physics, Vol. 80. dell'Antonio, G., Doplicher, S., Jona-Lasinio, G., (eds.). Berlin, Heidelberg, New York: Springer 1978

    Google Scholar 

  8. Göpfert, M.: Das Peierls-Argument für Z(2)-Gitter-Eichtheorien, Diplomarbeit Hamburg (1979) (unpublished)

  9. Fradkin, E., Shenker, S.: Phase diagrams of Lattice gauge theories with Higgs fields. Phys. Rev. D19, 3682 (1979)

    Google Scholar 

  10. Marra, R., Miracle-Solé, S.: On the statistical mechanics of the gauge invariant Ising model. Commun. Math. Phys.67, 233 (1979)

    Google Scholar 

  11. Buchholz, D., Fredenhagen, K.: Locality and the structure of particle states. Commun. Math. Phys.84, 1–54 (1982)

    Google Scholar 

  12. 't Hooft, G.: A property of electric and magnetic flux in nonabelian gauge theories. Nucl. Phys. B153, 141 (1979)

    Google Scholar 

  13. 't Hooft, G.: On the phase transition towards permanent quark confinement. Nucl. Phys. B138, 1 (1978)

    Google Scholar 

  14. Fredenhagen, K., Marcu, M.: Order parameters for lattice gauge theories with matter fields (to be published)

  15. Osterwalder, K., Seiler, E.: Gauge field theories on a lattice. Ann. Phys.110, 440 (1978)

    Google Scholar 

  16. Lüscher, M.: Construction of a selfadjoint, strictly positive transfer matrix for Euclidean lattice gauge theories. Commun. Math. Phys.54, 283 (1977)

    Google Scholar 

  17. Bratteli, O., Robinson, D.: Operator algebras and statistical mechanics. I, II. Berlin, Heidelberg, New York: Springer 1981

    Google Scholar 

  18. Cioranescu, I., Zsidó, L.: Analytic generators for one-parameter groups, Tôhoku Math. J.28, 327–362 (1976)

    Google Scholar 

  19. Reed, M., Simon, B.: Methods of modern mathematical physics. New York, San Francisco, London: Academic Press 1972

    Google Scholar 

  20. Glimm, J., Jaffe, A.: Quantum physics. A functional integral point of view, Berlin, Heidelberg, New York: Springer 1981

    Google Scholar 

  21. Fredenhagen, K.: On the existence of dynamics in Euclidean lattice gauge theories (to be published)

  22. Gantmacher, F.R.: Matrizenrechnung. Berlin: VEB Deutscher Verlag der Wissenschaften 1959

    Google Scholar 

  23. Ruelle, D.: Statistical mechanics. Reading, MA: Benjamin 1969

    Google Scholar 

  24. Bricmont, J., Lebowitz, J.L., Pfister, C.-E.: Non-translation invariant Gibbs states with coexisting phases. III. Analyticity properties. Commun. Math. Phys.69, 267–291 (1979)

    Google Scholar 

  25. Balian, R., Drouffe, J.M., Itzykson, C.: Gauge fields on a lattice. II. Gauge invariant Ising model. Phys. Rev. D11, 2098 (1975)

    Google Scholar 

  26. Streater, R.F., Wightman, A.S.: PCT, spin and statistics and all that. New York: Benjamin 1964

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by R. Haag

Heisenberg fellow

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fredenhagen, K., Marcu, M. Charged states in ℤ2 gauge theories. Commun.Math. Phys. 92, 81–119 (1983). https://doi.org/10.1007/BF01206315

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01206315

Keywords

Navigation