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Communications in Mathematical Physics

, Volume 86, Issue 1, pp 55–68 | Cite as

On the symplectic structure of general relativity

  • Abhay Ashtekar
  • Anne Magnon-Ashtekar
Article

Abstract

The relation between the symplectic structures on the canonical and radiative phase spaces of general relativity is exhibited.

Keywords

Neural Network Statistical Physic General Relativity Phase Space Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Dirac, P. A. M.: Proc. R. Soc. (London)A246, 333 (1958); Phys. Rev.114, 924 (1959); Lectures on quantum mechanics, New York: Yeshiva Univ. Press 1964Google Scholar
  2. 2.
    Bergmann, P. G.: Quantization of generally covariant field theories. ARL report 63–56 (1963)Google Scholar
  3. 3.
    Kuchar, K.: In: Quantum gravity. Isham, C. J., Penrose, R., Sciama, D. W. (eds.). Oxford: Oxford Univ. Press 1981Google Scholar
  4. 4.
    Arnowitt, R., Deser, S., Misner, C. W.: Phys. Rev.118, 1100 (1960); In: Gravitation an introduction to current research, Witten, L. (ed.). New York: Wiley, 1962Google Scholar
  5. 5.
    Regge, T., Teitelboim, C.: Ann. Phys.88, 286 (1974)Google Scholar
  6. 6.
    Ashtekar, A.: Phys. Rev. Lett.46, 573 (1981); In: Quantum gravity. Isham, C. J., Penrose, R., Sciama, D. W. (eds.). Oxford: Oxford Univ. Press 1981Google Scholar
  7. 7.
    Penrose, R.: Phys. Rev. Lett.10, 66 (1963); Proc. R. Soc. (London)A284, 159 (1965)Google Scholar
  8. 8.
    Sachs, R. K.: Phys. Rev.128, 2851 (1962)Google Scholar
  9. 9.
    Komar, A.: Phys. Rev.134, B1430 (1964)Google Scholar
  10. 10.
    Ashtekar, A., Streubel, M.: Proc. R. Soc. (London)A376, 585 (1981)Google Scholar
  11. 11.
    Ashtekar, A.: J. Math. Phys.22, 2885 (1981); Quantization of the radiative degrees of freedom of general relativity (preprint)Google Scholar
  12. 12.
    Buchholz D.: In: The proceedings of the 6th international conference on mathematical physics. New York: Springer 1981Google Scholar
  13. 13.
    Faddeev, L. D.: Theor. Math. Phys.1, 3 (1969)Google Scholar
  14. 14.
    Ashtekar, A., Geroch, R.: Rep. Prog. Phys.37, 1217–1219 and 1245–1247 (1974)Google Scholar
  15. 15.
    Fischer, A. E., Marsden, J. E.: In: General relativity. Hawking, S. W., Israel, W. (eds.), London: Cambridge Univ. Press 1978Google Scholar
  16. 16.
    Schmidt, B. G., Walker, M., Sommers, P.: Gen. Re. Grav.6, 489 (1975)Google Scholar
  17. 17.
    Geroch, R.: In: Asymptotic structure of space-time. Esposito, P., Witten, L., (eds.) New York: Plenum 1977Google Scholar
  18. 18.
    Friedman, J. L.: Commun. Math. Phys.62, 247 (1978)Google Scholar
  19. 19.
    Palmer, T. N.: J. Math. Phys.19, 2324 (1978)Google Scholar
  20. 20.
    Geroch, R., Xanthopoulos, B. C.: J. Math. Phys.19, 714 (1978)Google Scholar
  21. 21.
    Geroch, R., Horowitz, G. T.: Phys. Rev. Lett.40, 203 (1978)Google Scholar
  22. 22.
    Ashtekar, A.: In: General relativity and gravitation, one hundred years after the birth of Albert Einstein. Held, A. (ed.) New York: Plenum 1980Google Scholar
  23. 23.
    Porill, J., Steward, J. M.: Proc. R. Soc. (London)A376, 451, (1981)Google Scholar
  24. 24.
    Geroch, R.: J. Math. Phys.19, 1300 (1978)Google Scholar
  25. 25.
    Christodoulou, D.: The boost problem for weakly coupled quasilinear hyperbolic systems of second order. J. Math. Pure Appl. (to appear)Google Scholar
  26. 26.
    Choquet-Bruhat, Y., Christodoulou, D.: Elliptic systems in Hilbert spaces on manifolds which are euclidean at infinity. Acta Math. (to appear)Google Scholar
  27. 27.
    Christodoulou, D., O'Murchadha, N.: Commun. Math. Phys.80, 271 (1981)Google Scholar
  28. 28.
    Friedrich, H.: Proc. R. Soc. (London)A375, 169 (1981)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Abhay Ashtekar
    • 1
    • 2
  • Anne Magnon-Ashtekar
    • 3
  1. 1.Physics DepartmentSyracuse UniversitySyracuseUSA
  2. 2.Département de PhysiqueUniversité de Clermont-Fd.AubièreFrance
  3. 3.Département de MathématiquesUniversité de Clermont-Fd.AubièreFrance

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