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Motion in Quantum Gravity

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Mass and Motion in General Relativity

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 162))

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Abstract

We tackle the question of motion in Quantum Gravity: what does motion mean at the Planck scale? Although we are still far from a complete answer we consider here a toy model in which the problem can be formulated and resolved precisely. The setting of the toy model is a three-dimensional Euclidean gravity. Before studying the model in detail, we argue that Loop Quantum Gravity may provide a very useful approach when discussing the question of motion in Quantum Gravity.

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Notes

  1. 1.

    In fact, we know only one solution of all the constraints when there is a cosmological constant in the theory, known as the Kodama state [16]. This solution was discussed several years ago [27] but its physical interest remains minimal.

References

  1. R. Arnowitt, S.Deser, C.W.Misner, in Gravitation: an Introduction to Current Research, ed. by L. Witten (Wiley, New York, 1962), pp. 227–265

    Google Scholar 

  2. A. Ashtekar, Phys. Rev. Lett. 57, 2244 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  3. A. Ashtekar, J. Lewandowski, J. Math. Phys. 36, 2170 (1995)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. A. Ashtekar, J. Lewandowski, Class. Q. Grav. 21, R23 (2004); C. Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, 2004); T. Thiemann, Introduction to Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, 2004)

    Google Scholar 

  5. M. Banados, J. Zanelli, C. Teitelboim, Phys. Rev. Lett. 69, 1849 (1992)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. L. Barack, Chapter 12 of this volume

    Google Scholar 

  7. J.F. Barbero, Phys. Rev. D 51, 5507 (1995); G. Immirzi, Class. Q. Grav. 14, 177 (1997)

    Google Scholar 

  8. M. Bojowald, Phys. Rev. Lett. 86, 5227 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  9. E. Buffenoir, K. Noui, P. Roche, Class. Q. Grav. 19, 4953 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. S. Carlip, Quantum Gravity in 2+1 Dimensions (Cambridge University Press, Cambridge, 1998)

    Book  MATH  Google Scholar 

  11. J. Engle, R. Pereira, C. Rovelli, Phys. Rev. Lett. 99, 161301 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  12. L. Freidel, E. Livine, Class. Q. Grav. 23, 2021 (2006); L. Freidel, E. Livine, Phys. Rev. Lett. 96, 221301 (2006)

    Google Scholar 

  13. S. Holst, Phys. Rev. D 53, 5966 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  14. G. Immirzi, Nucl. Phys. Proc. Suppl. 57, 65 (1997)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. E. Joung, J. Mourad, K. Noui, J. Math. Phys. 50, 052503 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  16. H. Kodama, Phys. Rev. D 42, 2548 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  17. T.H. Koornwinder, N.M. Muller, J. Lie Theory 7, 101 (1997); Erratum, ibidem 8, 187 (1998); F.A. Bais, N.M. Muller, B.J. Schroers, Nucl. Phys. B 640, 3 (2002)

    Google Scholar 

  18. J. Lewandowski, A. Okolow, H. Sahlmann, T. Thiemann, Commun. Math. Phys. 267, 703 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  19. J.E. Moyal, Proc. Camb. Phil. Soc. 45, 99 (1949)

    Article  MATH  MathSciNet  Google Scholar 

  20. K. Noui, J. Math. Phys. 47 102501 (2006); K. Noui, Class. Q. Grav. 24, 329 (2007)

    Google Scholar 

  21. K. Noui, Phys. Rev. D 78, 105008 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  22. A. Perez, Class. Q. Grav. 20, R43 (2003)

    Article  MATH  ADS  Google Scholar 

  23. A. Perez, Phys. Rev. D 73, 044007 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  24. J. Polchinski, String Theory (Cambridge University Press, Cambridge, 1998)

    Book  Google Scholar 

  25. C. Rovelli, Phys. Rev. Lett. 14, 3288 (1996); K. Krasnov, Phys. Rev. D 55, 3505 (1997); A. Ashtekar, J. Baez, A. Corichi, K. Krasnov, Phys. Rev. Lett. 80, 904 (1998)

    Google Scholar 

  26. C. Rovelli, L. Smolin, Nucl. Phys. B 442, 593; Erratum, ibidem 456, 753 (1995); A. Ashtekar, J. Lewandowski, Class. Q. Grav. 14, A55 (1997); A. Ashtekar, J. Lewandowski, Adv. Theor. Math. Phys. 1, 388 (1997)

    Google Scholar 

  27. L. Smolin, arXiv:hep-th/0209079v1 (2002); E. Witten, arXiv:gr-qc/0306083v2 (2003); L. Freidel, L. Smolin, Class. Q. Grav. 21, 5685 (2004)

    Google Scholar 

  28. T. Thiemann, Class. Q. Grav. 15, 1281 (1998)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  29. T. Thiemann, Class. Q. Grav. 23, 2249 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  30. T. Thiemann, in Approaches to Fundamental Physics, ed. by I.-O. Stamatescu, E. Seiler, Lect. Notes Phys. 721 (Springer, Berlin, 2007), p. 185

    Google Scholar 

  31. E. Witten, Nucl. Phys. B. 311, 46 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  32. E. Witten, Commun. Math. Phys. 121, 351 (1989)

    Article  MATH  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Mathématiques et de Physique Théorique, UMR/CNRS 6083, Fédération Denis Poisson, Faculté des Sciences et Techniques, Parc de Grandmont, 37200, Tours, France

    Karim Noui

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  1. Karim Noui
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Correspondence to Karim Noui .

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Editors and Affiliations

  1. Institut d'Astrophysique de Paris, boulevard Arago 98bis, Paris, 75014, France

    Luc Blanchet

  2. Observatoire de la Cote d'Azur, Nice, France

    Alessandro Spallicci

  3. Dept. Physics, University of Florida, Gainesville, 32611-8440, Florida, USA

    Bernard Whiting

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Noui, K. (2009). Motion in Quantum Gravity. In: Blanchet, L., Spallicci, A., Whiting, B. (eds) Mass and Motion in General Relativity. Fundamental Theories of Physics, vol 162. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3015-3_19

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  • DOI: https://doi.org/10.1007/978-90-481-3015-3_19

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  • Print ISBN: 978-90-481-3014-6

  • Online ISBN: 978-90-481-3015-3

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