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Dynamics: Changing Atoms of Space–Time

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Quantum Cosmology

Part of the book series: Lecture Notes in Physics ((LNP,volume 835))

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Abstract

In the previous chapter, we have seen some aspects of spatial quantum geometry, with its characteristic discrete spectra, emerge even in isotropic models. Now, these spatial structures have to fit into a consistent quantum space–time which in a certain sense reduces to a solution of Einstein’s equation in a semiclassical or low-curvature limit. Only completing this most challenging step will make the theory one of quantum gravity, rather than of spatial quantum geometry.

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Notes

  1. 1.

    Notice that this sense of regularity does not by itself imply UV-finiteness in the usual meaning of quantum field theory. To test finiteness, one would have to compute scattering amplitudes of particle excitations on a quantum geometry state, which is difficult. It thus remains open how exactly a fundamentally finite version of loop quantum gravity could resolve non-renormalizability issues of perturbative quantum gravity.

  2. 2.

    These cannot be all contributions because higher-derivative terms of the metric do not arise by the holonomy replacement. See Chap. 13 for a general treatment of effective canonical dynamics which introduces new quantum degrees of freedom analogously to higher-derivative actions.

  3. 3.

    In such commutators in the full theory, a single \(V_v\) gives the same contribution as the volume operator of all of space: contributions from vertices not lying on the edges used for the holonomy in the commutator cancel. But this observation does not change the fact that inverse-triad operators receive contributions only from local vertex contributions of the volume operator. In reduced models, homogeneity implies that all vertex contributions must contribute equally; one can properly capture the full behavior only by using single vertex or plaquette contributions from the outset.

  4. 4.

    These models were initially introduced under the name “improved” quantization [37, 38], indicating advantages in certain regimes of low curvature and large volume. However, the modifications introduced in these models turned out to be rather ad-hoc. (To appreciate this realization, the models are sometimes called “improvised.”) By now, what goes by the name “improved dynamics” is under strong pressure from different types of inconsistencies. The improved dynamics is itself to be improved, giving the name a rather misleading connotation.

References

  1. Unruh, W.: Time, Gravity, and Quantum Mechanics pp. 23–94. Cambridge University Press, Cambridge (1997)

    Google Scholar 

  2. Weiss, N.: Phys. Rev. D 32, 3228 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  3. Jacobson, T.: (2000). hep-th/0001085

    Google Scholar 

  4. Bojowald, M., Singh, P., Skirzewski, A.: Phys. Rev. D 70, 124022 (2004). gr-qc/0408094

    Article  MathSciNet  ADS  Google Scholar 

  5. Rovelli, C., Smolin, L.: Phys. Rev. Lett. 72, 446 (1994). gr-qc/9308002

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Giesel, K., Thiemann, T.: Class Quantum Grav. 24, 2465 (2007). gr-qc/0607099

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Thiemann, T.: Class Quantum Grav. 15, 839 (1998). gr-qc/9606089

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Thiemann, T.: Class Quantum Grav. 15, 1281 (1998). gr-qc/9705019

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Thiemann, T.: Class Quantum Grav. 15, 875 (1998). gr-qc/9606090

    Article  MathSciNet  ADS  Google Scholar 

  10. Thiemann, T.: Phys. Lett. B 380, 257 (1996). gr-qc/9606088

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Lewandowski, J., Marolf, D.: Int. J Mod. Phys. D 7, 299 (1998). gr-qc/9710016

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Gambini, R., Lewandowski, J., Marolf, D., Pullin, J.: Int. J Mod. Phys. D 7, 97 (1998).gr-qc/9710018

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Ashtekar, A., Lewandowski, J., Sahlmann, H.: Class Quantum Grav. 20, L11 (2003). gr-qc/0211012

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Sahlmann, H., Thiemann, T.: Class Quantum Grav. 23, 867 (2006). gr-qc/0207030

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Bojowald, M.: Class Quantum Grav. 26, 075020 (2009). arXiv:0811.4129

    Article  MathSciNet  ADS  Google Scholar 

  16. Bojowald, M., Kastrup, H.A.: Class Quantum Grav. 17, 3009 (2000). hep-th/9907042

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Engle, J.: Class Quantum Grav. 23, 2861 (2006). gr-qc/0511107

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Engle, J.: Class Quantum Grav. 24, 5777 (2007). gr-qc/0701132

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. Koslowski, T.: (2006). gr-qc/0612138

    Google Scholar 

  20. Koslowski, T.: (2007). arXiv:0711.1098

    Google Scholar 

  21. Brunnemann, J., Fleischhack, C.: (2007). arXiv:0709.1621

    Google Scholar 

  22. Brunnemann, J., Koslowski, T.A. arXiv:1012.0053

    Google Scholar 

  23. Bojowald, M.: Class Quantum Grav. 19, 2717 (2002). gr-qc/0202077

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. Hinterleitner, F., Major, S.: Phys. Rev. D 68, 124023 (2003). gr-qc/0309035

    Article  MathSciNet  ADS  Google Scholar 

  25. Henriques, A.B.: Gen. Rel. Grav. 38, 1645 (2006). gr-qc/0601134

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. Varadarajan, M.: Class Quantum Grav. 26, 085006 (2009). arXiv:0812.0272

    Article  MathSciNet  ADS  Google Scholar 

  27. Bojowald, M.: Class Quantum Grav. 18, L109 (2001). gr-qc/0105113

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. Nelson, W., Sakellariadou, M.: Phys. Rev. D 76, 104003 (2007). arXiv:0707.0588

    Article  MathSciNet  ADS  Google Scholar 

  29. Nelson, W., Sakellariadou, M.: Phys. Rev. D 76, 044015 (2007). arXiv:0706.0179

    Article  MathSciNet  ADS  Google Scholar 

  30. Grain, J., Barrau, A., Gorecki, A.: Phys. Rev. D 79, 084015 (2009). arXiv:0902.3605

    Article  ADS  Google Scholar 

  31. Grain, J., Cailleteau, T., Barrau, A., Gorecki, A.: Phys. Rev. D 81, 024040 (2010). arXiv:0910.2892

    Article  ADS  Google Scholar 

  32. Shimano, M., Harada, T.: Phys. Rev. D 80, 063538 (2009). arXiv:0909.0334

    Article  ADS  Google Scholar 

  33. Bojowald, M.: Class Quantum Grav. 17, 1489 (2000). gr-qc/9910103

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. Bojowald, M.: Class Quantum Grav. 17, 1509 (2000). gr-qc/9910104

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. Bojowald, M.: Class Quantum Grav. 18, 1055 (2001). gr-qc/0008052

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. Bojowald, M.: Class Quantum Grav. 18, 1071 (2001). gr-qc/0008053

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. Ashtekar, A., Pawlowski, T., Singh, P.: Phys. Rev. D 74, 084003 (2006). gr-qc/0607039

    Article  MathSciNet  ADS  Google Scholar 

  38. Ashtekar, A., Wilson-Ewing, E.: Phys. Rev. D 79, 083535 (2009). arXiv:0903.3397

    Article  MathSciNet  ADS  Google Scholar 

  39. Bojowald, M., Calcagni, G.: JCAP 1103, 032 (2011). arXiv:1011.2779

    Google Scholar 

  40. Bojowald, M.: Phys. Rev. Lett. 86, 5227 (2001). gr-qc/0102069

    Article  MathSciNet  ADS  Google Scholar 

  41. Bojowald, M.: Proceedings of the XIIth Brazilian School on Cosmology and Gravitation. In: AIP Conference Proceedings, vol. 910, pp. 294–333 (2007). gr-qc/0702144

    Google Scholar 

  42. Bojowald, M.: Phys. Rev. Lett. 87, 121301 (2001). gr-qc/0104072

    Article  MathSciNet  ADS  Google Scholar 

  43. Bojowald, M.: Gen. Rel. Grav. 35, 1877 (2003). gr-qc/0305069

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Center for Gravitational Physics and Geometry, Pennsylvania State University, Davey Laboratory 104, University Park, PA, 16802-6300, USA

    Martin Bojowald

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  1. Martin Bojowald
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Bojowald, M. (2011). Dynamics: Changing Atoms of Space–Time. In: Quantum Cosmology. Lecture Notes in Physics, vol 835. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8276-6_4

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  • DOI: https://doi.org/10.1007/978-1-4419-8276-6_4

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