Skip to main content
Springer Nature Link
Log in

Canonical Quantization of Gravity

  • Conference paper
Relativity, Astrophysics and Cosmology

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 38))

  • 377 Accesses

Abstract

In Roman Catholic canon law permission of the bishop is required for the publication of any work on Sacred Scripture, dogmatic, moral or ascetical theology, or, in general, writings containing anything of peculiar significance to religion or morality (can. 1385, sec. 1).

Not to be confused with the canonical formalism which is the subject of these lectures.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

Bibliography

  1. Møller, C.: 1962, ‘The Energy-Momentum Complex in General Relativity and Related Problems’, in: Les théories relativistes de la Gravitation, (ed. by A. Lichnerowicz and M. A. Tonnelat), Centre Nationale de la Recherche Scientifique, Paris.

    Google Scholar 

  2. Rosenfeld, L.: 1963, Nucl. Phys. 40, 353.

    Article  MathSciNet  MATH  Google Scholar 

  3. DeWitt, B. S.: 1964, ‘Dynamical Theory of Groups and Fields’, in: Relativity, Groups and Topology (ed. by B. S. DeWitt and C. M. DeWitt), Gordon and Breach, New York-London.

    Google Scholar 

  4. DeWitt, B. S.: 1967, Phys. Rev. 162, 1195; 162, 1239.

    Article  ADS  Google Scholar 

  5. Dirac, P. A. M.: 1958, Proc. Roy. Soc. (London) A246, 326; A246, 333.

    MathSciNet  ADS  Google Scholar 

  6. Dirac, P. A. M.: 1959, Phys. Rev. 114, 924.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. DeWitt, B. S.: 1967, Phys. Rev. 160, 1113.

    Article  ADS  MATH  Google Scholar 

  8. Wheeler, J. A.: 1968, ‘Superspace and the Nature of Quantum Geometrodynamics’, in: Batelle Rencontres (ed. by C. DeWitt and J. A. Wheeler), Benjamin, New York.

    Google Scholar 

  9. Arnowitt, R. and Deser, S.: 1959, Phys. Rev. 113, 745.

    Google Scholar 

  10. Arnowitt, R., Deser, S., and Misner, C. W.: 1959, Phys. Rev. 116, 1322.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Arnowitt, R., Deser, S., and Misner, C. W.: 1960, Phys. Rev. 117, 1595.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Arnowitt, R., Deser, S., and Misner, C. W.: 1960, Nuovo Cim. 15, 487.

    Article  MATH  Google Scholar 

  13. Arnowitt, R., Deser, S., and Misner, C. W.: 1960, Phys Rev. Letters 4, 375.

    Article  ADS  Google Scholar 

  14. Arnowitt, R., Deser, S., and Misner, C. W.: 1960, Phys. Rev. 118, 1100.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Arnowitt, R., Deser, S., and Misner, C. W.: 1960, J. Math. Phys. 1, 434.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Arnowitt, R., Deser, S., and Misner, C. W.: 1960, Phys. Rev. 120, 313.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Arnowitt, R., Deser, S., and Misner, C. W.: 1960, Phys. Rev. 120, 321.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Arnowitt, R., Deser, S., and Misner, C. W.: 1960, Ann. Phys. 11, 116.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. Arnowitt, R., Deser, S., and Misner, C. W.: 1961, Nuovo Cim. 19, 668.

    Article  MathSciNet  MATH  Google Scholar 

  20. Arnowitt, R., Deser, S., and Misner, C. W.: 1961, Phys. Rev. 121, 1556.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Arnowitt, R., Deser, S., and Misner, C. W.: 1961, Phys. Rev. 122, 997.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. Arnowitt, R., Deser, S., and Misner, C. W.: 1962, ‘The Dynamics of General Relativity’, in: Gravitation: An Introduction to Current Research (ed. by L. Witten), Wiley, New York.

    Google Scholar 

  23. Mandelstam, S.: 1962, Ann. Phys. 19, 25.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. Mandelstam, S.: 1962, ‘Quantization of the Gravitational Field’, in: Relativistic Theories of Gravitation (ed. by L. Infeld), Pergamon, Gauthier-Villars, P. W. N., Warszawa.

    Google Scholar 

  25. Mandelstam, S.: 1968, Phys. Rev. 175, 1580.

    Article  ADS  Google Scholar 

  26. Schwinger, J.: 1966, Phys. Rev. 152, 1219.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. Schwinger, J.: 1967, Phys. Rev. 158, 1391.

    Article  ADS  Google Scholar 

  28. Schwinger, J.: 1968, Phys. Rev. 173, 1264.

    Google Scholar 

  29. Misner, C. W.: 1957, Rev. Mod. Phys. 29, 497.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Klauder, J. R.: 1962, Nuovo Cimenio 25, 542.

    Article  MathSciNet  MATH  Google Scholar 

  31. Fadeev, L. D. and Popov, V. N.: 1967, Phys. Letters 25B, 29.

    Google Scholar 

  32. Fadeev, L. D.: 1971, Actes, Congrès Intern. Math., Vol. 3, p. 35, Gauthier-Villars, Paris.

    Google Scholar 

  33. Leutwyler, H.: 1964, Phys. Rev. 134B, 1155.

    Article  MathSciNet  ADS  Google Scholar 

  34. Komar, A.: 1969, ‘On the Quantization of Gravitation’, in: Proceedings of the Eighth Annual Eastern Theoretical Physics Conference (ed. by F. Rohrlich), Syracuse University.

    Google Scholar 

  35. Penrose, R. and MacCallum, M. A. H. 1970, Twistor Theory: an Approach to the Quantization of Fields and Space-Time, mimeographed lecture notes, Institute of Theoretical Astronomy, Cambridge.

    Google Scholar 

  36. Brill, D. R. and Gowdy, R. H.: 1970, Progress Theor. Phys. 33, 413.

    Google Scholar 

  37. Bergmann, P. G.: 1956, Helv. Phys. Acta Suppl. 4, 79.

    Google Scholar 

  38. Schwinger, J.: 1963, Phys. Rev. 130, 1253; 1963, Phys. Rev. 132, 1317.

    Google Scholar 

  39. Peres, A.: 1968, Phys. Rev. 171, 1335.

    Article  ADS  Google Scholar 

  40. DeWitt, B. S.: 1970, Gen. Rel. Grav. 1, 181.

    Article  MathSciNet  ADS  Google Scholar 

  41. Wheeler, J. A.: 1964, ‘Geometrodynamics and the Issue of the Final State’, in: Relativity, Groups and Topology (ed. by B. S. DeWitt and C. M. DeWitt), Gordon and Breach, NewYork-London, pp. 328, 504.

    Google Scholar 

  42. Harrison, B. K., Thorne, K. S., Wakano, M., and Wheeler, J. A.: 1965, Gravitation Theory and Gravitational Collapse, The University of Chicago Press, Chicago-London, pp. 141–143.

    Google Scholar 

  43. Misner, C. W.: 1969, Phys. Rev. 186, 1319; 1969, Phys. Rev. 186, 1328.

    Article  ADS  MATH  Google Scholar 

  44. Ryan, M.: 1972, Hamiltonian Cosmology, Springer, Berlin-Heidelberg-New York.

    Google Scholar 

  45. Liang, E. P. T.: 1972, Phys. Rev. D5, 2458.

    ADS  Google Scholar 

  46. Deser, S.: 1967, Ann. Inst. Henri Poincaré 7, 149.

    MATH  Google Scholar 

  47. Kuchař, K.: 1970, J. Math. Phys. 11, 3322.

    Article  ADS  Google Scholar 

  48. York, J. W.: 1971, Phys. Rev. Letters 26, 1556.

    Article  MathSciNet  ADS  Google Scholar 

  49. York, J. W.: 1972, Phys. Rev. Letters 28, 1082.

    Article  ADS  Google Scholar 

  50. York, J. W.: 1972, J. Math. Phys. 13, 125.

    Article  MathSciNet  ADS  Google Scholar 

  51. York, J. W.: 1972, J. Math. Phys., in print.

    Google Scholar 

  52. Kuchař, K.: 1971, Phys. Rev. D4, 955.

    ADS  Google Scholar 

  53. Berger, B. K., Chitre, D. M., Monchrief, V. E., and Nutku, Y.: 1972, Phys. Rev. D5, 2467.

    ADS  Google Scholar 

  54. Kuchaf, K.: 1972, J. Math. Phys. 13, 768.

    Article  ADS  Google Scholar 

  55. Lichnerowicz, A.: 1955, Theories relativistes de la gravitation et de l’électromagtisme, Masson, Paris.

    Google Scholar 

  56. Adler, R., Bazin, M., and Schiffer, M.: 1965, Introduction to General Relativity, McGraw-Hill, New York, Chapter 7.

    MATH  Google Scholar 

  57. Lanczos, C.: 1949, The Variational Principles of Mechanics, University of Toronto Press, Toronto (4th edition 1970), chapters VI. 10, IX. 6-IX.10.

    MATH  Google Scholar 

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

    Google Scholar 

  59. Bergmann, P. G.: 1949, Phys. Rev. 75, 680.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  60. Dirac, P. A. M.: 1951, Canadian J. Math. 3, 1.

    Google Scholar 

  61. Moncrief, V.: 1972, Phys. Rev. D5, 277.

    MathSciNet  ADS  Google Scholar 

  62. Moncrief, V. and Teitelboim, C: 1972, Phys. Rev. D6, 966.

    MathSciNet  ADS  Google Scholar 

  63. Teitelboim, C.: 1972, Princeton University Preprint, submitted to Ann. Phys. N.Y.

    Google Scholar 

  64. Fischer, A. E. and Marsden, J. E.: 1972, J. Math. Phys. 13, 546.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  65. Misner, C. W.: 1972, ‘Minisuperspace’, in Magic Without Magic — J. A. Wheeler 60th Anniversary Volume (ed. by J. Klauder), Freeman, San Francisco.

    Google Scholar 

  66. Fischer, A. E.: 1970, ‘The Theory of Superspace’, in: Relativity (ed. by L. Witten), Plenum Press, New York-London.

    Google Scholar 

  67. Hojman, S., Kuchař, K., and Teitelboim, C.: 1973, paper in preparation.

    Google Scholar 

  68. Bergmann, P. G.: 1956, Nuovo Cimento 3, 1177.

    Article  MathSciNet  Google Scholar 

  69. Komar, A. B.: 1958, Phys. Rev. 111, 1182.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  70. Komar, A. B.: 1967, Phys. Rev. 164, 1595.

    Article  ADS  Google Scholar 

  71. Schweber, S. S.: 1961, An Introduction to Relativistic Quantum Field Theory, Row, Peterson, Evanston-Elmsford, Chapter 7, §5.

    Google Scholar 

  72. Novozhilov, Yu. V. and Tulub, A. V.: 1961, The Methods of Functionals in the Quantum Theory of Fields, Gordon and Breach, New York.

    Google Scholar 

  73. Higgs, P. W.: 1959, Phys. Rev. Letters 1, 373.

    Article  ADS  Google Scholar 

  74. Dirac, P. A. M.: 1969, ‘The Quantization of the Gravitational Field’, in: Contemporary Physics: Trieste Symposium 1968 (Vienna: IAEA), p. 539.

    Google Scholar 

  75. Misner, C.: 1970, ‘Classical and Quantum Dynamics of a Closed Universe’, in: Relativity (ed. by M. Carmeli, S. Fickler, and L. Witten), Plenum Press, New York.

    Google Scholar 

  76. Hughston, L. and Jacobs, K.: 1970, Astrophys. J. 160, 147.

    Article  MathSciNet  ADS  Google Scholar 

  77. Einstein, A. and Rosen, N.: 1937, J. Franklin Inst. 223, 43.

    Google Scholar 

  78. Rosen, N.: 1954, Bull. Res. Council Israel 3, 328.

    MathSciNet  Google Scholar 

  79. Weber, J. and Wheeler, J. A.: 1957, Rev. Mod. Phys. 29, 509.

    Google Scholar 

  80. Marder, L.: 1958, Proc. Roy. Soc. (London) A244, 524; A246, 133.

    MathSciNet  ADS  Google Scholar 

  81. Ehlers, J. and Kundt, W.: 1962, in: Gravitation: An Introduction to Current Research (ed. by L. Witten), Wiley, New York-London, Chapter 2.

    Google Scholar 

  82. Thorne, K. S.: 1965, Phys. Rev. B138, 251.

    Article  MathSciNet  ADS  Google Scholar 

  83. DeWitt, B. S.: 1962, ‘The Quantization of Geometry’, in: Gravitation: an Introduction to Current Research (ed. by L. Witten), Wiley, New York-London.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Joseph Henry Laboratories, Princeton University, Princeton, NJ, 08540, USA

    Karel Kuchař

Authors
  1. Karel Kuchař
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Theoretical Physics Institute, Physics Department, University of Alberta, Edmonton, Alberta, Canada

    Werner Israel

Rights and permissions

Reprints and permissions

Copyright information

© 1973 D. Reidel Publishing Company, Dordrecht-Holland

About this paper

Cite this paper

Kuchař, K. (1973). Canonical Quantization of Gravity. In: Israel, W. (eds) Relativity, Astrophysics and Cosmology. Astrophysics and Space Science Library, vol 38. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2639-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-2639-0_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-2641-3

  • Online ISBN: 978-94-010-2639-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics