Skip to main content
SpringerLink
Log in

An extension of the Dirac theory of constraints

  • Published:
Journal of Fixed Point Theory and Applications Aims and scope Submit manuscript

Abstract

Constructions introduced by Dirac for singular Lagrangians are extended and reinterpreted to cover cases when kernel distributions are either nonintegrable or of nonconstant rank, and constraint sets need not be closed.

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. E. Cartan, Lęcons sur les invariants intégraux. 3rd ed., Hermann, Paris, 1971.

  2. Chen H., Nester J., Yo H.-J.: Acausal PGT modes and the nonlinear constraint effect. Acta phys. Polon. B 29, 961–970 (1998)

    MATH  MathSciNet  Google Scholar 

  3. Dirac P.: Generalized Hamiltonian dynamics. Canad. J. Math. 2, 129–148 (1950)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dirac P.: Hamiltonian methods and quantum mechanics. Proc. Roy. Irish Acad. Sect. A 63, 49–59 (1964)

    MATH  MathSciNet  Google Scholar 

  5. P. Dirac, Lectures on Quantum Mechanics. Belfour Graduate School of Science, Yeshiva University, New York, 1964.

  6. M. Gotay, Presymplectic manifolds, geometric constriant theory and the Dirac-Bergmann theory of constraints. PhD thesis, University of Maryland, 1979.

  7. Gotay M., Nester J.: Presymplectic Lagrangian systems. II. The secondorder equation problem. Ann. Inst. H. Poincaré Sect. A 32, 1–13 (1980)

    MATH  MathSciNet  Google Scholar 

  8. Gotay M., Nester J.: Apartheid in the Dirac theory of constraints. J. Phys. A 17, 3063–3066 (1984)

    Article  MathSciNet  Google Scholar 

  9. Gotay M., Nester J., Hinds G.: Presymplectic manifolds and the Dirac-Bergmann theory of constraints. J. Math. Phys. 19, 2388–2399 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  10. A. Hanson, T. Regge and C. Teitelboim, Constrained Hamiltonian systems. Contributi del centro linceo interdisciplinare di scienze matematiche e loro applicazioni 22, Accademia Nazionale dei Lincei, Roma, 1976.

  11. Havelková M.: A geometric analysis of dynamical systems with singular Lagrangians. Commun. Math. 19, 169–178 (2011)

    MATH  MathSciNet  Google Scholar 

  12. E. Noether, Invariante variationsprobleme. Nachr. v. d. Ges. d. Wiss. zu Göttingen (1918), 235–257.

  13. Śniatycki J.: On the geometric structure of classical field theory in Lagrangian formulation. Math. Proc. Cambridge Philos. Soc. 68, 475–484 (1970)

    Article  MATH  Google Scholar 

  14. Śniatycki J.: Differential Geometry of Singular Spaces and Reduction of Symmetries. Cambridge University Press, Cambridge (2013)

    Book  Google Scholar 

  15. Whitney H.: Analytic extensions of differentiable functions defined in closed sets. Trans. Amer. Math. Soc. 36, 63–89 (1934)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Calgary, Calgary, Alberta, T2N 1N4, Canada

    Larry Bates & Jędrzej Śniatycki

Authors
  1. Larry Bates
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jędrzej Śniatycki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Larry Bates.

Additional information

To Yvonne Choquet-Bruhat on her 90th birthday

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bates, L., Śniatycki, J. An extension of the Dirac theory of constraints. J. Fixed Point Theory Appl. 14, 527–554 (2013). https://doi.org/10.1007/s11784-014-0173-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11784-014-0173-4

Mathematics Subject Classification

Keywords

Search

Navigation