Skip to main content
SpringerLink
Log in

Holography in the EPRL Model

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

In this research announcement, we propose a new interpretation of the Engle Pereira Rovelli (EPR) quantization of the Barrett-Crane (BC) model using a functor we call the time functor, which is the first example of a co-lax, amply renormalizable (claren) functor. Under the hypothesis that the universe is in the Kodama state, we construct a holographic version of the model. Generalisations to other claren functors and connections to model category theory are considered.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Engle, J., Pereira, R., Rovelli, C.: Flipped spinfoam vertex and loop gravity. Nucl. Phys. B 798(1–2), 251–290 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Livine, E.R., Speziale, S.: New spinfoam vertex for quantum gravity. Phys. Rev. D 76, 084028 (2007)

    Article  MathSciNet  ADS  Google Scholar 

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

  4. Barrett, J.W., Dowdall, R.J., Fairbairn, W.J., Gomes, H., Hellmann, F.: Asymptotic analysis of the Engle Pereira Rovelli Livine four-simplex amplitude. J. Math. Phys. 50, 112504 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  5. Barrett, J., Crane, L.: A Lorentzian signature model for quantum gravity. Class. Quantum Gravity 17, 3101–3118 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Bousso, R.: The holographic principle. Rev. Mod. Phys. 74, 825–874 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Crane, L.: 2d physics and 3d topology. Commun. Math. Phys. 135, 615–640 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Baez, J.C., Barrett, J.W.: Integrability for relativistic spin networks. Class. Quantum Gravity 18, 4683 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Crane, L., Yetter, D.: A categorical construction of 4D topological quantum field theories. Quantum Topol. 120–129 (1993)

  10. Witten, E.: Topological quantum field theory and the Jones polynomial. Commun. Math. Phys. 121, 351 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Kodama, H.: Holomorphic wave function of the Universe. Phys. Rev. D 42, 2548–2565 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  12. Bekenstein, J.D.: Holographic bound from second law of thermodynamics. Phys. Lett. B 481(2–4), 339–345 (2000)

    MathSciNet  ADS  MATH  Google Scholar 

  13. Smolin, L.: An invitation to loop quantum gravity (2004). hep-th/0408048

  14. Crane, L.: Relational spacetime, model categories and quantum gravity. Int. J. Mod. Phys. A 24(15), 2753–2775 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Bousfield, A.K., Kan, D.M.: Homotopy limits, completions and localizations (1972)

  16. Sullivan, D.: Infinitesimal computations in topology. Publ. Math. IHES 47(1), 269–331 (1977)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, KSU, Manhattan, USA

    Louis Crane

Authors
  1. Louis Crane
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Louis Crane.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Crane, L. Holography in the EPRL Model. Found Phys 42, 909–917 (2012). https://doi.org/10.1007/s10701-012-9630-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-012-9630-3

Keywords

Search

Navigation