Communications in Mathematical Physics

, Volume 46, Issue 2, pp 183–206 | Cite as

A canonical structure for classical field theories

  • Jerzy Kijowski
  • Wiktor Szczyrba


A general scheme of constructing a canonical structure (i.e. Poisson bracket, canonical fields) in classical field theories is proposed. The theory is manifestly independent of the particular choice of an initial space-like surface in space-time. The connection between dynamics and canonical structure is established. Applications to theories with a gauge and constraints are of special interest. Several physical examples are given.


Neural Network Statistical Physic Field Theory Complex System Special Interest 
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  1. 1.
    Bałaban, T., Rączka, R.: Second quantization of non-linear relativistic wave equations, Part I: Canonical formalism (preprint)Google Scholar
  2. 2.
    Białynicki-Birula, I.: Nuovo Cimento35, 697 (1965)Google Scholar
  3. 3.
    Białynicki-Birula, I., Iwiński, Z.: Reports Math. Phys.4, 139 (1973)Google Scholar
  4. 4.
    Bourbaki, N.: Topologie générale. Paris: 1960Google Scholar
  5. 5.
    Dedecker, P.: Calcul des variations, formes différentielles et champs géodésiques. Colloque International de Géometrie Différentielle. Strassbourg: 1953Google Scholar
  6. 6.
    Gawędzki, K.: Reports Math. Phys.3, 307 (1972)Google Scholar
  7. 7.
    Gawędzki, K.: Fourier-like kernels in geometric quantization, Dissertationes Math., to appearGoogle Scholar
  8. 8.
    Jörgens, K.: Math. Z.77, 295 (1961)Google Scholar
  9. 9.
    Kijowski, J.: Commun. Math. Phys.30, 99 (1973)Google Scholar
  10. 10.
    Kijowski, J., Szczyrba, W.: On inductive differential manifolds (in preparation)Google Scholar
  11. 11.
    Kostant, B.: Quantization and unitary representations. Lecture Notes in Math.170, p. 87. Berlin-Heidelberg-New York: Springer 1970Google Scholar
  12. 12.
    Moravetz, C. S., Strauss, W. A.: Comm. Pure Appl. Math.25, 1 (1972)Google Scholar
  13. 13.
    Renouard, P.: Variétés sympléctiques et quantification. Orsay: Thése (1969)Google Scholar
  14. 14.
    Segal, I. E.: Mathematical problems of relativistic physics. Proceedings of the Summer Seminar. Boulder, Colorado 1960Google Scholar
  15. 15.
    Sternberg, S.: Lectures on differential geometry, New York: 1964Google Scholar
  16. 16.
    Szczyrba, W.: Lagrangian formalism in the classical field theory. Annal. Polon. Math.32 (1975) (to appear)Google Scholar
  17. 17.
    Sternberg, S., Goldschmidt, H.: Annal. Instit. Fourier23, 203–267 (1973)Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Jerzy Kijowski
    • 1
    • 2
  • Wiktor Szczyrba
    • 1
    • 2
  1. 1.Institute of Mathematical Methods of PhysicsWarsaw UniversityWarsawPoland
  2. 2.Institute of Mathematics of the Polish Academy of SciencesWarsawPoland

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