Skip to main content
SpringerLink
Log in

Generalized Noether theorems in canonical formalism for field theories and their applications

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

A generalization of Noether's first theorem in phase space for an invariant system with a singular Lagrangian in field theories is derived and a generalization of Noether's second theorem in phase space for a noninvariant system in field theories is deduced. A counterexample is given to show that Dirac's conjecture fails. Some preliminary applications of the generalized Noether second theorem to the gauge field theories are discussed. It is pointed out that for certain systems with a noninvariant Lagrangian in canonical variables for field theories there is also a Dirac constraint. Along the trajectory of motion for a gauge-invariant system some supplementary relations of canonical variables and Lagrange multipliers connected with secondary first-class constraints are obtained.

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

  • Allcock, G. R. (1975).Philosophical Transactions of the Royal Society A,279, 585.

    Google Scholar 

  • Castellani, L. (1982).Annals of Physics,143, 357.

    Google Scholar 

  • Cawley, R. (1979).Physical Review Letters,42, 413.

    Google Scholar 

  • Cawley, R. (1980).Physical Review D,21, 2988.

    Google Scholar 

  • Costa, H. E. V., Girotto, H. O., and Simoes, T. J. M. (1985).Physical Review D,32, 405.

    Google Scholar 

  • Dirac, P. A. M. (1964).Lectures on Quantum Mechanics, Yeshiva University Press, New York.

    Google Scholar 

  • Di Stefano, R. (1983).Physical Review D,27, 1752.

    Google Scholar 

  • Djukic, D. S. (1974).Archives of Mechanics,26, 243.

    Google Scholar 

  • Frenkel, A. (1980).Physical Review D,21, 2986.

    Google Scholar 

  • Grácia, X., and Pons, J. M. (1988).Annals of Physics,187, 355.

    Google Scholar 

  • Li, Z. P. (1982).Physica Energiae et Physica Nuclearis,6, 555.

    Google Scholar 

  • Li, Z. P. (1991).Journal of Physics A: Mathematical and General,24, 4261.

    Google Scholar 

  • Li, Z. P., and Li, X. (1991).International Journal of Theoretical Physics,30, 225.

    Google Scholar 

  • Qi, Z. (1990).International Journal of Theoretical Physics,29, 1309.

    Google Scholar 

  • Sugano, R. (1982).Progress of Theoretical Physics,68, 1377.

    Google Scholar 

  • Sugano, R., and Kamo, H. (1982).Progress of Theoretical Physics,67, 1966.

    Google Scholar 

  • Sugano, R., and Kimura, T. (1983a).Progress of Theoretical Physics,69, 252.

    Google Scholar 

  • Sugano, R., and Kimura, T. (1983b).Progress of Theoretical Physics,69, 1256.

    Google Scholar 

  • Sugano, R., and Kimura, T. (1983c).Journal of Physics A: Mathematical and General,16, 4417.

    Google Scholar 

  • Zhao, B. H., and Yan, M. L. (1978).Physica Energiae et Physica Nuclearis,2, 501.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. World Laboratory, CCAST, P.O. Box 8730, 100080, Beijing

    Zi-ping Li

  2. Department of Applied Physics, Beijing Polytechnic University, 100022, Beijing, China

    Zi-ping Li

Authors
  1. Zi-ping Li
    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

Li, Zp. Generalized Noether theorems in canonical formalism for field theories and their applications. Int J Theor Phys 32, 201–215 (1993). https://doi.org/10.1007/BF00674405

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00674405

Keywords

Search

Navigation