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.
Similar content being viewed by others
References
L. Réau,L'Art russe, II, 18n, Paris, 1921.
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).
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).
P. A. M. Dirac,Proc. Roy. Soc. London A 246, 333 (1958).
P. G. Bergmannet al., Phys. Rev. 80, 81 (1950).
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.
K. Kuchař,J. Math. Phys. 13, 768 (1972).
K. Kuchař,J. Math. Phys. 17, 792 (1976).
K. Kuchař,J. Math. Phys. 17, 777 (1976).
K. Kuchař,J. Math. Phys. 18, 1589 (1977).
P. A. M. Dirac,Lectures on Quantum Mechanics, Belfer Graduate School of Science, Yeshiva, New York (1964).
B. S. DeWitt,Phys. Rev. 160, 1113 (1967).
K. Kuchař,J. Math. Phys. 22, 2640 (1981).
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).
C. J. Isham and K. V. Kuchař,Ann. Phys. (N.Y.),164, 288 (1985).
C. J. Isham and K. V. Kuchař,Ann. Phys. (N.Y.),164, 316 (1985).
J. Evans,John Ruskin (Oxford University Press, New York, 1954).
C. Lanczos,The Variational Principles of Mechanics (University of Toronto Press, Toronto, 1970), 4th edn., Chap. V, §6.
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).
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).
K. Kuchař,J. Math. Phys. 17, 801 (1976), §12.
C. Teitelboim,Ann. Phys. (N.Y.) 79, 542 (1973).
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).
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.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kuchař, K.V. Canonical geometrodynamics and general covariance. Found Phys 16, 193–208 (1986). https://doi.org/10.1007/BF01889472
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01889472