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SIGMA, 2012, Volume 8, 002, 29 pages (Mi sigma679)  

This article is cited in 18 scientific papers (total in 18 papers)

Discretisations, constraints and diffeomorphisms in quantum gravity

Benjamin Bahra, Rodolfo Gambinib, Jorge Pullinc

a Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
b Instituto de Física, Facultad de Ciencias, Universidad de la República, Iguá 4225, CP 11400 Montevideo, Uruguay
c Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USA

Abstract: In this review we discuss the interplay between discretization, constraint implementation, and diffeomorphism symmetry in Loop Quantum Gravity and Spin Foam models. To this end we review the Consistent Discretizations approach, which is an application of the master constraint program to construct the physical Hilbert space of the canonical theory, as well as the Perfect Actions approach, which aims at finding a path integral measure with the correct symmetry behavior under diffeomorphisms.

Keywords: quantum gravity, diffeomorphisms, constraints, consistent discretizations, gauge symmetries, perfect actions, renormalization.

DOI: https://doi.org/10.3842/SIGMA.2012.002

Full text: PDF file (517 kB)
Full text: http://emis.mi.ras.ru/.../002
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Bibliographic databases:

ArXiv: 1111.1879
MSC: 37M99; 70H45; 81T17; 82B28; 83C27; 83C45
Received: November 9, 2011; in final form December 31, 2011; Published online January 8, 2012
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Citation: Benjamin Bahr, Rodolfo Gambini, Jorge Pullin, “Discretisations, constraints and diffeomorphisms in quantum gravity”, SIGMA, 8 (2012), 002, 29 pp.

Citation in format AMSBIB
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\by Benjamin Bahr, Rodolfo Gambini, Jorge Pullin
\paper Discretisations, constraints and diffeomorphisms in quantum gravity
\jour SIGMA
\yr 2012
\vol 8
\papernumber 002
\totalpages 29
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Dittrich B., Steinhaus S., “Path integral measure and triangulation independence in discrete gravity”, Phys Rev D, 85:4 (2012), 044032  crossref  adsnasa  isi  elib  scopus
    2. Dittrich B., “From the Discrete to the Continuous: Towards a Cylindrically Consistent Dynamics”, New J. Phys., 14 (2012), 123004  crossref  mathscinet  isi  scopus
    3. Borja E.F., Garay I., Strobel E., “Revisiting the Quantum Scalar Field in Spherically Symmetric Quantum Gravity”, Class. Quantum Gravity, 29:14 (2012), 145012  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Dittrich B., Hohn Ph.A., “Canonical Simplicial Gravity”, Class. Quantum Gravity, 29:11 (2012), 115009  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Cartin D., “Conserved Quantities in Isotropic Loop Quantum Cosmology”, EPL, 98:3 (2012), 30007  crossref  adsnasa  isi  scopus
    6. Dittrich B., Hohn Ph.A., “Constraint Analysis for Variational Discrete Systems”, J. Math. Phys., 54:9 (2013), 093505  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Carlip S., “Challenges for Emergent Gravity”, Stud. Hist. Philos. Mod. Phys., 46:B (2014), 200–208  crossref  mathscinet  zmath  isi  elib  scopus
    8. Dittrich B., Steinhaus S., “Time Evolution as Refining, Coarse Graining and Entangling”, New J. Phys., 16 (2014), 123041  crossref  isi  scopus
    9. Hoehn Ph.A., “Classification of Constraints and Degrees of Freedom For Quadratic Discrete Actions”, J. Math. Phys., 55:11 (2014), 113506  crossref  mathscinet  zmath  adsnasa  isi  scopus
    10. Hoehn Ph.A., “Quantization of Systems With Temporally Varying Discretization. II. Local Evolution Moves”, J. Math. Phys., 55:10 (2014), 103507  crossref  mathscinet  zmath  adsnasa  isi  scopus
    11. Hoehn Ph.A., “Quantization of Systems With Temporally Varying Discretization. i. Evolving Hilbert Spaces”, J. Math. Phys., 55:8 (2014), 083508  crossref  mathscinet  zmath  adsnasa  isi  scopus
    12. Haggard H.M., Han M., Kaminski W., Riello A., “Sl(2, C) Chern-Simons Theory, a Non-Planar Graph Operator, and 4D Quantum Gravity With a Cosmological Constant: Semiclassical Geometry”, Nucl. Phys. B, 900 (2015), 1–79  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    13. Steinhaus S., “Coupled Intertwiner Dynamics: a Toy Model For Coupling Matter To Spin Foam Models”, Phys. Rev. D, 92:6 (2015), 064007  crossref  adsnasa  isi  scopus
    14. Hoehn Ph.A., “Canonical Linearized Regge Calculus: Counting Lattice Gravitons With Pachner Moves”, Phys. Rev. D, 91:12 (2015), 124034  crossref  mathscinet  adsnasa  isi  scopus
    15. Berra-Montiel J., Rosales-Quintero J.E., “Discrete Canonical Analysis of Three-Dimensional Gravity With Cosmological Constant”, Int. J. Mod. Phys. A, 30:15 (2015), 1550080  crossref  mathscinet  zmath  adsnasa  isi  scopus
    16. Bahr B., Steinhaus S., “Numerical Evidence for a Phase Transition in 4D Spin-Foam Quantum Gravity”, Phys. Rev. Lett., 117:14 (2016), 141302  crossref  isi  elib  scopus
    17. B. Bahr, “On background-independent renormalization of spin foam models”, Class. Quantum Gravity, 34:7 (2017), 075001  crossref  mathscinet  zmath  isi  scopus
    18. S. Lanery, T. Thiemann, “Projective limits of state spaces IV. Fractal label sets”, J. Geom. Phys., 123 (2018), 127–155  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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