Skip to main content
SpringerLink
Log in

Applications of the canonical-transformation theory for presymplectic systems

Применения теории канонических преобразований для пресимплекных систем

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

Two applications of the canonical-transformation theory for presymplectic systems developed in a previous paper are presented: a new approach to the extended formalism for the time-dependent systems and the relativistic free massive point. For this last system some examples of canonical transformations are constructed explicitly.

Riassunto

Sono presentate 2 applicazioni della teoria delle trasformazioni canoniche per sistemi presimplectici: un nuovo approccio per l'esteso formalismo per i sistemi tempo-dipendente e per il punto relativistico libero e con massa. Per quest'ultimo sistema sono costruiti esplicitamente alcuni esempi di trasformazioni canoniche.

Резюме

Рассматриваются два применения теории канонических преобразований для пресимплексных систем, развитой в предыдушей работе. Предлагается новый подход к обобшенному формализму для зависящих от времени систем и релятивистской свободной массивной точке. Для последней системы в явном виде конструируются некоторые примеры канонических преобразований.

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. R. Abraham andJ. E. Marsden:Foundations of Mechanics 2nd edition (Benjamin-Cummings, Reading, Mass., 1978).

    MATH  Google Scholar 

  2. S. Sternberg:Lectures on Differential Geometry (Prentice-Hall Inc., Englewood Cliffs, N. J., 1983).

    MATH  Google Scholar 

  3. J. M. Souriau:Structure des Systemes Dinamiques (Dunod, Paris, 1974).

    MATH  Google Scholar 

  4. J. Sniatycki:Ann. Inst. Henri Poincaré A,20, 365 (1974).

    MathSciNet  MATH  Google Scholar 

  5. M. J. Gotay:Presymplectic manifolds, geometric constraint theory and the Dirac-Bergmann theory of constraints, Ph.D. Thesis, University of Maryland (1979).

  6. M. J. Gotay, J. M. Nester andG. Hinds:J. Math. Phys. (N. Y.),19(11), 2388 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  7. M. J. Bergvelt:Yang-Mills theories as constrained Hamiltonian Systems, preprint I.F.T.A. 83-5 (1983).

  8. J. F. Cariñena, J. Gomis, L. A. Ibort andN. Román-Roy:J. Math. Phys. (N. Y.) 26(8), 1961 (1985).

    Article  ADS  MATH  Google Scholar 

  9. M. Asorey, J. F. Cariñena andL. A. Ibort:J. Math. Phys. (N. Y.),24, 2745 (1983).

    Article  ADS  MATH  Google Scholar 

  10. A. Weinstein:Lectures on Symplectic Manifolds, C.B.M.S. Regional Conf. Ser. Math. 29 (1979).

  11. M. J. Gotay:Proc. Am. Math. Soc.,84, 111 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  12. C. M. Marle:Asterisque,107–108, 69 (1983).

    MathSciNet  Google Scholar 

  13. S. Shanmugadhasan:J. Math. Phys. (N. Y.),14, 677 (1973).

    Article  ADS  MATH  Google Scholar 

  14. L. Hwa Chung:Proc. R. Soc. London, Ser. A,12, 237 (1947).

    Google Scholar 

  15. J. Gomis, J. Llosa andN. Román-Roy:J. Math. Phys. (N. Y.),25, 1348 (1984).

    Article  ADS  MATH  Google Scholar 

  16. H. Goldstein:Classical Mechanics, 2nd edition (Addison-Wesley, Reading, Mass., 1980).

    MATH  Google Scholar 

  17. D. Dominici andJ. Gomis:J. Math. Phys. (N. Y.),21, 2124 (1980).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. R. Kuwabara:Rep. Math. Phys.,19, 27 (1984).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. L. A. Ibort:Estructura geométrica de los sistemas con simetría en mecánica clásica y teoría clásica de campos, Ph.D. Thesis, Universitat de Zaragoza (1984).

  20. E. C. G. Sudarshan andN. Mukunda:Classical Dynamics: A Modern Perspective (Wiley, New York, N. Y., 1974).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Física Teórica, Facultad de Ciencias, Universital de Zaragoza, Zaragoza, Spain

    J. F. Cariñena & L. A. Ibort

  2. Departament de Física Teórica, Universitat de Barcelona, Barcelona, Spain

    J. Gomis

  3. Departament de Física, E.T.S.E.I.B., Universitat Politécnica de Catalunya, Barcelona, Spain

    N. Román-Roy

Authors
  1. J. F. Cariñena
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. A. Ibort
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Gomis
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. N. Román-Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Traduzione a cura della Redazione.

Переведено редакцией.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cariñena, J.F., Ibort, L.A., Gomis, J. et al. Applications of the canonical-transformation theory for presymplectic systems. Nuov Cim B 98, 172–196 (1987). https://doi.org/10.1007/BF02721479

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02721479

PACS. 03.20

Search

Navigation