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Canonical Gravity: From Classical to Quantum pp 113–149Cite as

Quantization of systems with constraints

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References

  1. C.J. Isham: Conceptual and Geometrical Problems in Quantum Gravity. In: H. Mitter, H. Gausterer (Eds.) “Recent Aspects of Quantum Fields”. Springer-Verlag, Berlin (1991) 123–230.

    Google Scholar 

  2. K.V. Kuchař: Time and Interpretations of Quantum Gravity. In: Proceedings of the 4th Canadian Conference on General Relativity and Relativistic Astrophysics. World Scientific, Singapore (1992) 211–314.

    Google Scholar 

  3. C.J. Isham: Canonical Quantum Gravity and the Problem of Time. In: “Integrable Systems, Quantum Groups, and Quantum Field Theories”. Kluwer Academic Publishers, London (1993) 157–288.

    Google Scholar 

  4. A. Ashtekar: Lectures on Non-Perturbative Canonical Gravity. World Science, Singapore, 1991.

    Google Scholar 

  5. R.S. Tate: An Algebraic Approach to the Quantization of Constrained Systems: Finite Dimensional Examples. Ph.D. Thesis, Syracues University, 1992.

    Google Scholar 

  6. A. Ashtekar, R. Tate, C. Uggla: Int.J.Mod.Phys. D2, 15 (1993).

    Google Scholar 

  7. A. Ashtekar, R.S. Tage, C. Uggla: Minisuperspaces: Symmetries and Quantization. Preprint SU-CP-92/2-5 (1993).

    Google Scholar 

  8. K.V. Kuchař, in Conceptual Problems of Quantum Gravity Eds. A. Ashtekar and J. Stachel. Birkhauser, Boston, 1991.

    Google Scholar 

  9. P. Hájiček and B.S. Kay: Quantum Collapse of a Self-Gravitating Shell: Construction of a Quantum Mechanics. Preprint, Santa Barbara, 1993.

    Google Scholar 

  10. P.A.M. Dirac: Lectures on Quantum Mechanics. New York, Yeshiva University, 1964.

    Google Scholar 

  11. P.A.M. Dirac: Rev.Mod.Phys. 21, 392 (1949).

    Google Scholar 

  12. W.G. Unruh and R.M. Wald: Phys.Rev. D40, 2598 (1989).

    Google Scholar 

  13. C. Rovelli: Phys.Rev. D42, 2638 (1990); Phys.Rev. D43, 442 (1991).

    Google Scholar 

  14. K.V. Kuchař: Canonical Quantization of Generally Covariant Systems. Talk at International Conference on Gravitation and Cosmology, Goa, India, 14–19 Dec. 1987.

    Google Scholar 

  15. R. Abraham and J.E. Marsden: Foundation of Mechanics. London, Benjamin, 1985.

    Google Scholar 

  16. P. Hájiček and K.V. Kuchař: Phys.Rev. D41, 1091 (1990).

    Google Scholar 

  17. P. Hájicek: Class. Quantum Gravity 7, 871 (1990)

    Google Scholar 

  18. I.M. Gel'fand and Ya. Vilenkin: Generalized Functions. Vol. IV. Academic Press, New York, 1965.

    Google Scholar 

  19. A. Rendall: Unique Determination of an Inner Product by Adjointness Relation in the Algebra of Quantum Observables. Class. Quantum Grav. 10 (1993) 2261–2269.

    Google Scholar 

  20. B.C. DeWitt: in Relativity, Groups and Topology. Eds. C. DeWitt and B.C. DeWitt. New York, Gordon & Breach, 1964.

    Google Scholar 

  21. A.O. Barut and R. Raczka: Theory of Group Representations and Applications. Warshawa, Polish Scientific Publishers, 1977.

    Google Scholar 

  22. I.M. Gel'fand and C.E. Shilov: Generalized Functions. Vol. I. Academic Press, New York, 1964.

    Google Scholar 

  23. K.V. Kuchař: J.Math.Phys. 22, 2640 (1981).

    Google Scholar 

  24. B.S. Kay: Commun.Math. Phys. 62, 55 (1978).

    Google Scholar 

  25. S.J. Avis, C.J. Isham and D. Storey: Phys.Rev. D18, 3565 (1978).

    Google Scholar 

  26. P. Hájicek: Commun.Math.Phys. 150, 545 (1992).

    Google Scholar 

  27. P. Hájiček, B.S. Kay and K.V. Kuchař: Phys.Rev. D46, 5439 (1992).

    Google Scholar 

  28. W. Israel: Nuovo Cimento 44B, 1 (1966)

    Google Scholar 

  29. K.V. Kuchař: Czech.J.Phys. B18, 435 (1968).

    Google Scholar 

  30. A. Sommerfeld: Wave Mechanics. Dutton, New York, 1930.

    Google Scholar 

  31. H. Bethe: Intermediate Quantum Mechanics. Benjamin, New York, 1965.

    Google Scholar 

  32. M. Reed and B. Simon: Methods of Modern Mathematical Physics. Vol. I and II. Academic Press, New York, 1973.

    Google Scholar 

  33. J.D. Bjorken and S.D. Drell: Relativistic Quantum Mechanics. McGraw-Hill, New York, 1964.

    Google Scholar 

  34. E. Verlinde and H. Verlinde: A Unitary S-Matrix for 2d Black Hole Formation and Evaporation. Preprint, PUPT-1380, IASSNS-HEP-93/8 (1993).

    Google Scholar 

  35. E. Verlinde, H. Verlinde and D. Schoutens: Quantum Black Hole Evaporation. Preprint, PUPT-1395, IASSNS-HEP-93/25 (1993)

    Google Scholar 

  36. A. Mikovic: Non-Perturbative Two-Dimensional Dilation Gravity. Preprint, Imperial-TP/92-93/44.

    Google Scholar 

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Authors
  1. Petr Hájiček
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J. Ehlers H. Friedrich

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© 1994 Springer-Verlag

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Hájiček, P. (1994). Quantization of systems with constraints. In: Ehlers, J., Friedrich, H. (eds) Canonical Gravity: From Classical to Quantum. Lecture Notes in Physics, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58339-4_17

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  • DOI: https://doi.org/10.1007/3-540-58339-4_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58339-4

  • Online ISBN: 978-3-540-48665-7

  • eBook Packages: Springer Book Archive

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