Foundations of Physics Letters

, Volume 9, Issue 2, pp 157–164 | Cite as

On the quantization of general relativity in anholonomic variables

  • H. -H. v. Borzeszkowski
  • V. de Sabbata
  • C. Sivaram
  • H. -J. Treder
Article
  • 17 Downloads

Abstract

In discussing Bohr-Sommerfeld-like quantum rules for gravity, it is argued that Einstein's Riemannian theory of general relativity rather leads to a quantum field-mechanics than to a quantum-field theory of gravity. We construct the canonically conjugate coordinates and momenta of this gravito-dynamics in the framework of the Einstein-Cartan teleparallelism.

Key words

quantum gravity Einstein-Cartan theories Bohr-Sommerfeld quantum rules 

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References

  1. 1.
    E. Cartan,J. de Math. pur. et app. 6, 1–119 (1927);Lecons sur la geometrie des espaces de Riemann, 2nd ed. (Gauthier-Villars, Paris, 1946).Google Scholar
  2. 2.
    A. Einstein,Math. Ann. 103, 687–697 (1930).Google Scholar
  3. 3.
    J. W. Moffat, inGravitation 1990, Proceedings of the Banff Summer Institute, Banff, Alberta, 1990, R. D. Mann and P. Wesson, eds. (World Scientific, Singapore, 1991); cf. also the literature cited therein.Google Scholar
  4. 4.
    F. W. Hehl, J. D. McCrea, E. W. Mielke, and Y. Ne'eman, “Metric-affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance,”Phys. Rep. 258 (1995) pp. 1–171; cf. also the literature cited therein.CrossRefGoogle Scholar
  5. 5.
    V. de Sabbata and S. Sivaram,Found. Phys. Lett. 5, 579 (1992).CrossRefGoogle Scholar
  6. 6.
    V. de Sabbata, S. Sivaram, H.-H. v. Borzeszkowski, and H.-J. Treder,Ann. Phys. (Leipzig) 48, 497 (1991).Google Scholar
  7. 7.
    A. Messiah,Quantum Mechanics, Vol. I (North-Holland, Amsterdam, 1961).Google Scholar
  8. 8.
    H.-J. Treder, H.-H. v. Brozeszkowski, A. van der Merwe, and W. Yourgrau,Fundamental Principles of General Relativity Theories (Plenum, New York, 1980).Google Scholar
  9. 9.
    E. Cartan, inElie Cartan — Albert Einstein, Letters on Absolute Parallelism, 1929–1932, J. Leroy and J. Ritter, eds. (Princeton University Press, Princeton, 1979).Google Scholar
  10. 10.
    C. Møller,Mat. Fys. Skr. Dan. Vid. Selskab. 1 (10) (1961); inEntstehung, Entwicklung und Perspektiven der Einsteinschen Gravitationstheorie, H.-J. Treder, ed. (Akademie-Verlag, Berlin, 1966).Google Scholar
  11. 11.
    H.-H. v. Borzeszkowski and H.-J. Treder,Gen. Rel. Grav. 25, 391 (1993).Google Scholar
  12. 12.
    L. Rosenfield, inEnstehung, Entwicklung und Perspektiven der Einsteinschen Gravitationstheorie, loc cit. Google Scholar
  13. 13.
    N. Bohr and L. Rosenfield,Det. Kgl. Dan. Vid. Selskab., Matfys., Medd. XII (8) (Copenhagen, 1933).Google Scholar
  14. 14.
    L. P. Eisenhart,Non-Riemannian Geometry (Am. Math. Soc., New York, 1927).Google Scholar
  15. 15.
    L. P. Eisenhart,Riemannian Geometry, 2nd. edn. (Princeton University Press, Princeton, 1949).Google Scholar
  16. 16.
    J. A Schouten,Ricci-Calculus (Springer, Berlin, 1954).Google Scholar
  17. 17.
    J. A. Wheeler,Einstein's Vision (Springer, Berlin, 1968).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • H. -H. v. Borzeszkowski
    • 1
  • V. de Sabbata
    • 2
  • C. Sivaram
    • 3
  • H. -J. Treder
    • 4
  1. 1.TU Berlin, Institut für Theoretische Physik, “Gravitationsprojekt”PotsdamGermany
  2. 2.Dipartimento di FisicaUniversita di Ferrara, Istituto di Fisica NucleareSezione di FerraraItaly
  3. 3.Indian Institute of AstrophysicsBangaloreIndia
  4. 4.PotsdamGermany

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