General information
Latest issue
Impact factor

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS


Personal entry:
Save password
Forgotten password?

SIGMA, 2012, Volume 8, 009, 50 pages (Mi sigma686)  

This article is cited in 12 scientific papers (total in 12 papers)

Lessons from toy-models for the dynamics of loop quantum gravity

Valentin Bonzoma, Alok Laddhab

a Perimeter Institute for Theoretical Physics, 31 Caroline St. N, ON N2L 2Y5, Waterloo, Canada
b Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, PA 16802-6300, USA

Abstract: We review some approaches to the Hamiltonian dynamics of (loop) quantum gravity, the main issues being the regularization of the Hamiltonian and the continuum limit. First, Thiemann's definition of the quantum Hamiltonian is presented, and then more recent approaches. They are based on toy models which provide new insights into the difficulties and ambiguities faced in Thiemann's construction. The models we use are parametrized field theories, the topological BF model of which a special case is three-dimensional gravity which describes quantum flat space, and Regge lattice gravity.

Keywords: Hamiltonian constraint, loop quantum gravity, parametrized field theories, topological BF theory, discrete gravity.


Full text: PDF file (818 kB)
Full text:
References: PDF file   HTML file

Bibliographic databases:

ArXiv: 1110.2157
MSC: 83C45; 57R56; 83C27
Received: October 11, 2011; in final form February 24, 2012; Published online March 7, 2012

Citation: Valentin Bonzom, Alok Laddha, “Lessons from toy-models for the dynamics of loop quantum gravity”, SIGMA, 8 (2012), 009, 50 pp.

Citation in format AMSBIB
\by Valentin Bonzom, Alok Laddha
\paper Lessons from toy-models for the dynamics of loop quantum gravity
\jour SIGMA
\yr 2012
\vol 8
\papernumber 009
\totalpages 50

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kinjal Banerjee, Gianluca Calcagni, Mercedes Martín-Benito, “Introduction to loop quantum cosmology”, SIGMA, 8 (2012), 016, 73 pp.  mathnet  crossref  mathscinet
    2. Sergei Alexandrov, Marc Geiller, Karim Noui, “Spin foams and canonical quantization”, SIGMA, 8 (2012), 055, 79 pp.  mathnet  crossref  mathscinet
    3. E. Alesci, F. Cianfrani, “Quantum-reduced loop gravity: cosmology”, Phys. Rev. D, 87:8 (2013), 083521  crossref  mathscinet  adsnasa  isi  elib  scopus
    4. V. Bonzom, B. Dittrich, “Dirac's discrete hypersurface deformation algebras”, Class. Quantum Gravity, 30:20 (2013), 205013  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. A. Henderson, A. Laddha, C. Tomlin, “Constraint algebra in loop quantum gravity reloaded. I. Toy model of a $\mathrm{U}(1)^3$ gauge theory”, Phys. Rev. D, 88:4 (2013), 044028  crossref  adsnasa  isi  scopus
    6. Ch. Charles, E. R. Livine, “Ashtekar–Barbero holonomy on the hyperboloid: Immirzi parameter as a cutoff for quantum gravity”, Phys. Rev. D, 92:12 (2015), 124031  crossref  mathscinet  adsnasa  isi  elib  scopus
    7. Ph. A. Hoehn, “Canonical linearized Regge calculus: counting lattice gravitons with Pachner moves”, Phys. Rev. D, 91:12 (2015), 124034  crossref  mathscinet  adsnasa  isi  scopus
    8. J. Ben Achour, M. Geiller, K. Noui, Ch. Yu, “Testing the role of the Barbero–Immirzi parameter and the choice of connection in loop quantum gravity”, Phys. Rev. D, 91:10 (2015), 104016  crossref  mathscinet  adsnasa  isi  scopus
    9. A. Ashtekar, M. Reuter, C. Rovelli, “From general relativity to quantum gravity”, General Relativity and Gravitation, A Centennial Perspective, eds. A. Ashtekar, B. Berger, J. Isenberg, M. Maccallum, Cambridge Univ Press, 2015, 553–611  crossref  mathscinet  isi  scopus
    10. A. Feller, E. R. Livine, “Ising spin network states for loop quantum gravity: a toy model for phase transitions”, Class. Quantum Gravity, 33:6 (2016), 065005  crossref  mathscinet  zmath  adsnasa  isi  scopus
    11. Ch. Charles, E. R. Livine, “The Fock space of loopy spin networks for quantum gravity”, Gen. Relativ. Gravit., 48:8 (2016), 113  crossref  mathscinet  zmath  isi  elib  scopus
    12. A. Feller, E. R. Livine, “Surface state decoherence in loop quantum gravity, a first toy model”, Class. Quantum Gravity, 34:4 (2017), 045004  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
    Number of views:
    This page:116
    Full text:21

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019