Skip to main content
Log in

On the quantization of general relativity in anholonomic variables

  • Published:
Foundations of Physics Letters

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  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. A. Einstein,Math. Ann. 103, 687–697 (1930).

    Google Scholar 

  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. 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.

    Article  Google Scholar 

  5. V. de Sabbata and S. Sivaram,Found. Phys. Lett. 5, 579 (1992).

    Article  Google Scholar 

  6. V. de Sabbata, S. Sivaram, H.-H. v. Borzeszkowski, and H.-J. Treder,Ann. Phys. (Leipzig) 48, 497 (1991).

    Google Scholar 

  7. A. Messiah,Quantum Mechanics, Vol. I (North-Holland, Amsterdam, 1961).

    Google Scholar 

  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. 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. 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).

  11. H.-H. v. Borzeszkowski and H.-J. Treder,Gen. Rel. Grav. 25, 391 (1993).

    Google Scholar 

  12. L. Rosenfield, inEnstehung, Entwicklung und Perspektiven der Einsteinschen Gravitationstheorie, loc cit.

  13. N. Bohr and L. Rosenfield,Det. Kgl. Dan. Vid. Selskab., Matfys., Medd. XII (8) (Copenhagen, 1933).

  14. L. P. Eisenhart,Non-Riemannian Geometry (Am. Math. Soc., New York, 1927).

    Google Scholar 

  15. L. P. Eisenhart,Riemannian Geometry, 2nd. edn. (Princeton University Press, Princeton, 1949).

    Google Scholar 

  16. J. A Schouten,Ricci-Calculus (Springer, Berlin, 1954).

    Google Scholar 

  17. J. A. Wheeler,Einstein's Vision (Springer, Berlin, 1968).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

v. Borzeszkowski, H.H., de Sabbata, V., Sivaram, C. et al. On the quantization of general relativity in anholonomic variables. Found Phys Lett 9, 157–164 (1996). https://doi.org/10.1007/BF02186258

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02186258

Key words

Navigation