Advertisement

Foundations of Physics

, Volume 16, Issue 3, pp 193–208 | Cite as

Canonical geometrodynamics and general covariance

  • Karel V. Kuchař
Part II. Invited Papers Dedicated To John Archibald Wheeler

Abstract

By extending geometrodynamical phase space by embeddings and their conjugate momenta, one can homomorphically map the Lie algebra of space-time diffeomorphisms into the Poisson algebra of dynamical variables on the extended phase space.

Keywords

Covariance Phase Space Dynamical Variable Extended Phase General Covariance 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. Réau,L'Art russe, II, 18n, Paris, 1921.Google Scholar
  2. 2.
    J. A. Wheeler, “Geometrodynamics and the Issue of the Final State,” inRelativity, Groups and Topology, C. DeWitt and B. DeWitt, eds. (Gordon and Breach, New York, 1964).Google Scholar
  3. 3.
    B. S. DeWitt, “Dynamical Theory of Groups and Fields,” inRelativity, Groups and Topology, C. DeWitt and B. DeWitt, eds. (Gordon and Breach, New York, 1964).Google Scholar
  4. 4.
    P. A. M. Dirac,Proc. Roy. Soc. London A 246, 333 (1958).Google Scholar
  5. 5.
    P. G. Bergmannet al., Phys. Rev. 80, 81 (1950).CrossRefGoogle Scholar
  6. 6.
    R. Arnowitt, S. Deser, and C. W. Misner, “The Dynamics of General Relativity,” inGravitation: An Introduction to Current Research, L. Witten, ed. (Wiley, New York, 1962), and references cited therein.Google Scholar
  7. 7.
    K. Kuchař,J. Math. Phys. 13, 768 (1972).CrossRefGoogle Scholar
  8. 8.
    K. Kuchař,J. Math. Phys. 17, 792 (1976).CrossRefGoogle Scholar
  9. 9.
    K. Kuchař,J. Math. Phys. 17, 777 (1976).CrossRefGoogle Scholar
  10. 10.
    K. Kuchař,J. Math. Phys. 18, 1589 (1977).CrossRefGoogle Scholar
  11. 11.
    P. A. M. Dirac,Lectures on Quantum Mechanics, Belfer Graduate School of Science, Yeshiva, New York (1964).Google Scholar
  12. 12.
    B. S. DeWitt,Phys. Rev. 160, 1113 (1967).CrossRefGoogle Scholar
  13. 13.
    K. Kuchař,J. Math. Phys. 22, 2640 (1981).CrossRefGoogle Scholar
  14. 14.
    C. J. Isham, “Global and Topological Aspects of Quantum Gravity,” inRelativity, Groups and Topology II, B. S. DeWitt and R. Stora, eds. (North-Holland, Amsterdam, 1984).Google Scholar
  15. 15.
    C. J. Isham and K. V. Kuchař,Ann. Phys. (N.Y.),164, 288 (1985).CrossRefGoogle Scholar
  16. 16.
    C. J. Isham and K. V. Kuchař,Ann. Phys. (N.Y.),164, 316 (1985).CrossRefGoogle Scholar
  17. 17.
    J. Evans,John Ruskin (Oxford University Press, New York, 1954).Google Scholar
  18. 18.
    C. Lanczos,The Variational Principles of Mechanics (University of Toronto Press, Toronto, 1970), 4th edn., Chap. V, §6.Google Scholar
  19. 19.
    K. Kuchař, “Canonical Methods of Quantization,” inQuantum Gravity II: A Second Oxford Symposium, C. J. Isham, R. Penrose, and D. Sciama, eds. (Clarendon Press, Oxford, 1981).Google Scholar
  20. 20.
    K. Kuchař,J. Math. Phys. 17, 801 (1976);19, 390 (1978);25, 1647 (1982); J. B. Hartle and K. V. Kuchař,J. Math. Phys. 25, 57 (1984).CrossRefGoogle Scholar
  21. 21.
    K. Kuchař,J. Math. Phys. 17, 801 (1976), §12.CrossRefGoogle Scholar
  22. 22.
    C. Teitelboim,Ann. Phys. (N.Y.) 79, 542 (1973).CrossRefGoogle Scholar
  23. 23.
    B. S. DeWitt, “The Spacetime Approach to Quantum Field Theory,” inRelativity, Groups and Topology II, B. S. DeWitt and R. Stora, eds. (North-Holland, Amsterdam, 1984).Google Scholar
  24. 24.
    P. A. M. Dirac, “Versatility of Niels Bohr,” inNiels Bohr, S. Rozental, ed. (North-Holland, Amsterdam, 1967);The Reader's Digest Treasury of Modern Quotations (Crowell, New York, 1975), p. 510.Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • Karel V. Kuchař
    • 1
  1. 1.Department of PhysicsThe University of UtahSalt Lake City

Personalised recommendations