Skip to main content
SpringerLink
Log in

Non-Abelianizable First Class Constraints

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

Abstract

We study the necessary and sufficient conditions on Abelianizable first class constraints. The necessary condition is derived from topological considerations on the structure of the gauge group. The sufficient condition is obtained by applying the implicit function theorem in calculus and studying the local structure of gauge orbits. Since the sufficient condition is necessary for the existence of proper gauge fixing conditions, we conclude that in the case of a finite set of non-Abelianizable first class constraints, the Faddeev-Popov determinant is vanishing for any choice of subsidiary constraints. This result is explicitly examined for the SO(3) gauge invariant model.

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. Dirac, P.A.M.: Can. J. Math. 2, 129 (1950); Proc. R. Soc. London Ser. A 246, 326 (1958); Lectures on Quantum Mechanics. New York: Yeshiva University Press, 1964

    MATH  Google Scholar 

  2. Batlle, C., Gomis, J., Gracia, X., Pons, J.M.: J. Math. Phys. 30 (6), 1345 (1989); Pons, J.M., Garcia, J.A.: Int. J. Mod. Phys. A 15, 4681 (2000)

    MATH  Google Scholar 

  3. Henneaux, M.: Phys. Rep. 126, 1 (1985)

    Google Scholar 

  4. Henneaux, M., Teitelboim, C.: Quantization of Gauge System. Princeton, NJ: Princeton University Press, 1992

  5. Goldberg, J., Newman, E.T., Rovelli, C.: J. Math. Phys. 32, 2739 (1991)

    MATH  Google Scholar 

  6. Bergman, P.G., Goldberg, I.: Phys. Rev. 98, 531 (1955); Bergman, P.G.: ibid. 98, 544 (1955)

    Google Scholar 

  7. Gogilidze, S.A., Khvedelidze, A.M., Pervushin, V.N.: J. Math. Phys. 37, 1760 (1996)

    MATH  Google Scholar 

  8. Loran, F.: Phys. Lett. B547, 63 (2002)

  9. Loran, F.: Phys. Lett. B554, 207 (2003)

  10. Battle, C., Gomis, J., Pons, J.M., Roman-Roy, N.: J. Math. Phys. 27 (12), 2953 (1986)

    Google Scholar 

  11. Govaerts, J.: Hamiltonian Quantisation and Constrained Dynamics. Leuven Notes in Theoretical and Mathematical Physics, Leuven: Leuven University Press, 1991

  12. Munkres, J.R.: Topology, A First Course. Englewood Cliffs, NJ: Prentice-Hall, Inc, 1975

  13. Govaerts, J., Klauder, J.R.: Ann. Phys. 274, 251 (1999)

    MATH  Google Scholar 

  14. Friedberg, R., Lee, T.D., Pang, Y., Ren, H.C.: Ann. Phys. 246, 381 (1996)

    MATH  Google Scholar 

  15. John, F.: Partial Differential Equations. Vol. 1, Fourth Edition, New York: Springer-Verlag New York Inc., 1981

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Isfahan University of Technology (IUT), Isfahan, Iran

    Farhang Loran

Authors
  1. Farhang Loran
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Farhang Loran.

Additional information

Communicated by G.W. Gibbons

Acknowledgement The financial support of Isfahan University of Technology (IUT) is acknowledged.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Loran, F. Non-Abelianizable First Class Constraints. Commun. Math. Phys. 254, 167–178 (2005). https://doi.org/10.1007/s00220-004-1248-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00220-004-1248-7

Keywords

Search

Navigation