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Quantum Spacetime

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Springer Handbook of Spacetime

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Abstract

The recent progress towards the construction of a quantum theory of gravity has been impressive, in particular thanks to the Fairbairn–Meusburger– Han theorems on the finiteness of the spinfoam expansion [1] [2], and the Freidel-Conrady–Barrett etal–Han theorems on its classical limit [1] [3] [4] [5]. This advance yields a very good understanding of how quantum spacetime can be described. I summarize the result of these developments, focusing on the conceptual aspects of the problem: the emerging nature of quantum spacetime, and the revision of the concepts of space and time it demands.

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Abbreviations

EPRL:

Engle-Pereira-CR-Livine

GR:

general relativity

QCD:

quantum chromodynamics

QED:

quantum electrodynamics

References

  1. W.J. Fairbairn, C. Meusburger: Quantum deformation of two four-dimensional spin foam models, J.Math.Phys. 53, 022501 (2012)

    Google Scholar 

  2. M. Han: 4-Dimensional spin-foam model with quantum Lorentz group, J. Math. Phys. 52, 072501 (2011)

    Google Scholar 

  3. F. Conrady, L. Freidel: Path integral representation of spin foam models of 4-D gravity, Class. Quantum Gravity 25, 245010 (2008)

    Google Scholar 

  4. J.W. Barrett, R.J. Dowdall, W.J. Fairbairn, F. Hellmann, R. Pereira: Lorentzian spin foam amplitudes: Graphical calculus and asymptotics, Class. Quantum Gravity 27, 165009 (2010)

    Google Scholar 

  5. M. Han, M. Zhang: Asymptotics of spinfoam amplitude on simplicial manifold: Lorentzian theory, Class. Quantum Gravity 30, 165012 (2013)

    Google Scholar 

  6. C. Rovelli: Quantum Gravity (Cambridge Univ. Press, Cambridge 2004)

    Google Scholar 

  7. C. Rovelli: Relational quantum mechanics, Int. J. Theor. Phys. 35(9), 1637 (1996)

    Google Scholar 

  8. E. Bianchi: Talk at the 2012 Marcel Grossmann meeting (July 2012)

    Google Scholar 

  9. C. Rovelli: Discretizing parametrized systems: The magic of Ditt-invariance, arXiv:1107.2310 (2011)

    Google Scholar 

  10. A. Ashtekar: New variables for classical and quantum gravity, Phys. Rev. Lett. 57, 2244 (1986)

    Google Scholar 

  11. E. Bianchi, P. Dona, S. Speziale: Polyhedra in loop quantum gravity, Phys. Rev. D83, 044035 (2011)

    Google Scholar 

  12. L. Freidel, S. Speziale: Twisted geometries: A geometric parametrisation of SU(2) phase space, Phys. Rev. D82, 084040 (2010)

    Google Scholar 

  13. M. Dupuis, J.P. Ryan, S. Speziale: Discrete gravity models and loop quantum gravity: A short review, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)8 (2012)

    Google Scholar 

  14. Rovelli: Zakopane lectures in loop gravity, Proc. 3rd Quantum Gravity Quantum Geometry School 003 (2011), arXiv:1102.3660

    Google Scholar 

  15. C. Rovelli, L. Smolin: Spin networks and quantum gravity, Phys. Rev. D52, 5743 (1995)

    Google Scholar 

  16. C. Rovelli, L. Smolin: Discreteness of area and volume in quantum gravity, Nucl. Phys. B442, 593 (1995)

    Google Scholar 

  17. A. Ashtekar, J. Lewandowski: Quantum theory of geometry. I: Area operators, Class. Quantum Gravity 14, A55 (1997)

    Google Scholar 

  18. B. Bahr, F. Hellmann, W. Kaminski, M. Kisielowski, J. Lewandowski: Operator spin foam models, Class. Quantum Gravity 28, 105003 (2011)

    Google Scholar 

  19. W. Wieland: Complex Ashtekar variables and reality conditions for Holst’s action, Annales Henri Poincare 13, 425 (2012)

    Google Scholar 

  20. J. Engle, E.R. Livine, R. Pereira, C. Rovelli: LQG vertex with finite Immirzi parameter, Nucl. Phys. B799, 136 (2008)

    Google Scholar 

  21. J. Engle, R. Pereira, C. Rovelli: The loop-quantum-gravity vertex-amplitude, Phys. Rev. Lett. 99, 161301 (2007)

    Google Scholar 

  22. E.R. Livine, S. Speziale: A new spinfoam vertex for quantum gravity, Phys. Rev. D76, 084028 (2007)

    Google Scholar 

  23. L. Freidel, K. Krasnov: A new spin foam model for 4-D gravity, Class. Quantum Gravity 25, 125018 (2008)

    Google Scholar 

  24. R. Pereira: Lorentzian LQG vertex amplitude, Class. Quantum Gravity 25, 085013 (2008)

    Google Scholar 

  25. A. Perez: The spin foam approach to quantum gravity, Living Rev. Relativ. 16, 3 (2013)

    Google Scholar 

  26. M. Han: Cosmological constant in LQG vertex amplitude, Phys. Rev. D84, 064010 (2011)

    Google Scholar 

  27. C. Rovelli: A Generally covariant quantum field theory and a prediction on quantum measurements of geometry, Nucl. Phys. B405, 797 (1993)

    Google Scholar 

  28. L. Smolin: Finite diffeomorphism invariant observables in quantum gravity, Phys. Rev. D49, 4028 (1994)

    Google Scholar 

  29. C. Rovelli: Comment on ‘Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?’ by B. Dittrich and T. Thiemann, arXiv:0708.2481 (2007)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Centre de Physique Théorique de Luminy, Aix-Marseille University, Luminy, 13288, Marseille, France

    Carlo Rovelli

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  1. Carlo Rovelli
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Correspondence to Carlo Rovelli .

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Editors and Affiliations

  1. Department of Physics, Pennsylvania State University, 16802, University Park, PA, USA

    Abhay Ashtekar

  2. Institute for Foundational Studies Hermann Minkowski, Montreal, Quebec, Canada

    Vesselin Petkov

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Rovelli, C. (2014). Quantum Spacetime. In: Ashtekar, A., Petkov, V. (eds) Springer Handbook of Spacetime. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41992-8_36

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  • DOI: https://doi.org/10.1007/978-3-642-41992-8_36

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  • Online ISBN: 978-3-642-41992-8

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