CoChat
Sign Up
Cited by 84Noncommutative and Quantum Gravity TheoriesRelativity and Gravitational TheoryBlack Holes and Theoretical Physics

Towards the QFT on curved spacetime limit of QGR: I. A general scheme

Open access
Sahlmann, H, Thiemann, T·2006·Classical and Quantum Gravity
DOI 10.1088/0264-9381/23/3/019
Open this paper in CoChat — free accountOpen PDF

Abstract

In this article and a companion paper we address the question of how one might obtain the semiclassical limit of ordinary matter quantum fields (QFT) propagating on curved spacetimes (CST) from full fledged Quantum General Relativity (QGR), starting from first principles. We stress that we do not claim to have a satisfactory answer to this question, rather our intention is to ignite a discussion by displaying the problems that have to be solved when carrying out such a program. In the present paper we propose a scheme that one might follow in order to arrive at such a limit. We discuss the technical and conceptual problems that arise in doing so and how they can be solved in principle. As to be expected, completely new issues arise due to the fact that QGR is a background independent theory. For instance, fundamentally the notion of a photon involves not only the Maxwell quantum field but also the metric operator - in a sense, there is no photon vacuum state but a "photon vacuum operator"! While in this first paper we focus on conceptual and abstract aspects, for instance the definition of (fundamental) n-particle states (e.g. photons), in the second paper we perform detailed calculations including, among other things, coherent state expectation values and propagation on random lattices. These calculations serve as an illustration of how far one can get with present mathematical techniques. Although they result in detailed predictions for the size of first quantum corrections such as the gamma-ray burst effect, these predictions should not be taken too seriously because a) the calculations are carried out at the kinematical level only and b) while we can classify the amount of freedom in our constructions, the analysis of the physical significance of possible choices has just begun.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1088/0264-9381/23/3/019

Cites

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Early model calculations suggest that Lorentz-invariance-violation effects may arise from a quantum-gravity granularity of spacetime measured at rest by a preferred frame.

    “In the absence of detailed formulations, certain early pioneering model calculations [192] (see also general treatment [340, 341]) indicate the possibility for certain Lorentz-invariance-violation (LIV) effects associated to a quantum-gravity granularity of spacetime measured at rest by a preferred frame of observers.”

    From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [340]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

The citation lists haven’t been fetched yet

References 41 · Cited by 84

Research works printed but not linked: 38

  1. [1][1] H. Sahlmann and T. Thiemann, Towards the QFT on curved spacetime limit of QGR. II: A concrete implementation , http://arXiv.org/abs/gr-qc/0207031 . - · arXiv
  2. [3][3] C. Rovelli, Loop quantum gravity , Living Rev. Rel. 1 (1998) 1 [ http://arXiv.org/abs/gr-qc/9710008 ]. - · arXiv
  3. [6][6] C. Rovelli, The century of the incomplete revolution: Searching for general relativistic quantum field theory , J. Math. Phys. 41 (2000) 3776-3800 [ http://arXiv.org/abs/hep-th/9910131 ]. - · arXiv
  4. [7][7] A. Ashtekar, C. Rovelli and L. Smolin, Weaving a classical geometry with quantum threads , Phys. Rev. Lett. 69 (1992) 237-240 [ http://arXiv.org/abs/hep-th/9203079 ]. - · arXiv
  5. [8][8] L. Bombelli, Statistical geometry of random weave states , http://arXiv.org/abs/gr-qc/0101080 . - · arXiv
  6. [9][9] T. Thiemann, Gauge field theory coherent states (GCS). I: General properties , Class. Quant. Grav. 18 (2001) 2025-2064 [ http://arXiv.org/abs/hep-th/0005233 ]. - · arXiv
  7. [10][10] T. Thiemann and O. Winkler, Gauge field theory coherent states (GCS). II: Peakedness properties , Class. Quant. Grav. 18 (2001) 2561-2636 [ http://arXiv.org/abs/hep-th/0005237 ]. - · arXiv
  8. [11][11] T. Thiemann and O. Winkler, Gauge field theory coherent states (GCS) III: Ehrenfest theorems , Class. Quant. Grav. 18 (2001) 4629-4682 [ http://arXiv.org/abs/hep-th/0005234 ]. - · arXiv
  9. [14][14] A. Ashtekar, C. Rovelli and L. Smolin, Gravitons and loops , Phys. Rev. D44 (1991) 1740-1755 [ http://arXiv.org/abs/hep-th/9202054 ]. - · arXiv
  10. [15][15] M. Varadarajan, Gravitons from a loop representation of linearised gravity , http://arXiv.org/abs/gr-qc/0204067 . - · arXiv
  11. [16][16] M. Varadarajan, Photons from quantized electric flux representations , Phys. Rev. D64 (2001) 104003 [ http://arXiv.org/abs/gr-qc/0104051 ]. - · arXiv
  12. [17][17] M. Varadarajan, Fock representations from U(1) holonomy algebras , Phys. Rev. D61 (2000) 104001 [ http://arXiv.org/abs/gr-qc/0001050 ]. - · arXiv
  13. [18][18] A. Ashtekar and J. Lewandowski, Relation between polymer and Fock excitations , Class. Quant. Grav. 18 (2001) L117-L128 [ http://arXiv.org/abs/gr-qc/0107043 ]. - · arXiv
  14. [20][20] G. Amelino-Camelia, Quantum-gravity phenomenology: Status and prospects , http://arXiv.org/abs/gr-qc/0204051 . - · arXiv
  15. [21][21] R. Gambini and J. Pullin, Nonstandard optics from quantum spacetime , Phys. Rev. D59 (1999) 124021 [ http://arXiv.org/abs/gr-qc/9809038 ]. - · arXiv
  16. [22][22] J. Alfaro, H. A. Morales-Tecotl and L. F. Urrutia, Quantum gravity corrections to neutrino propagation , Phys. Rev. Lett. 84 (2000) 2318-2321 [ http://arXiv.org/abs/gr-qc/9909079 ]. - · arXiv
  17. [23][23] J. Alfaro, H. A. Morales-Tecotl and L. F. Urrutia, Loop quantum gravity and light propagation , http://arXiv.org/abs/hep-th/0108061 . - · arXiv
  18. [24][24] J. Alfaro and G. Palma, Loop quantum gravity corrections and cosmic rays decays , http://arXiv.org/abs/hep-th/0111176 . - · arXiv
  19. [26][26] T. Thiemann, QSD III: Quantum constraint algebra and physical scalar product in quantum general relativity , Class. Quant. Grav. 15 (1998) 1207-1247 [ http://arXiv.org/abs/gr-qc/9705017 ]. - · arXiv
  20. [27][27] T. Thiemann, QSD V: Quantum gravity as the natural regulator of matter quantum field theories , Class. Quant. Grav. 15 (1998) 1281-1314 [ http://arXiv.org/abs/gr-qc/9705019 ]. - · arXiv
  21. [28][28] T. Thiemann, Quantum spin dynamics (QSD) , Class. Quant. Grav. 15 (1998) 839-873 [ http://arXiv.org/abs/gr-qc/9606089 ]. - · arXiv
  22. [30][30] C. Di Bartolo, R. Gambini, J. Griego and J. Pullin, Canonical quantum gravity in the Vassiliev invariants arena. I: Kinematical structure , Class. Quant. Grav. 17 (2000) 3211-3238 [ http://arXiv.org/abs/gr-qc/9911009 ]. - · arXiv
  23. [31][31] C. Di Bartolo, R. Gambini, J. Griego and J. Pullin, Canonical quantum gravity in the Vassiliev invariants arena. II: Constraints, habitats and consistency of the constraint algebra , Class. Quant. Grav. 17 (2000) 3239-3264 [ http://arXiv.org/abs/gr-qc/9911010 ]. - · arXiv
  24. [32][32] M. Bojowald, Isotropic loop quantum cosmology , Class. Quant. Grav. 19 (2002) 2717-2742 [ http://arXiv.org/abs/gr-qc/0202077 ]. - · arXiv
  25. [33][33] M. Bojowald, The inverse scale factor in isotropic quantum geometry , Phys. Rev. D64 (2001) 084018 [ http://arXiv.org/abs/gr-qc/0105067 ]. - · arXiv
  26. [34][34] A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourao and T. Thiemann, Quantization of diffeomorphism invariant theories of connections with local degrees of freedom , J. Math. Phys. 36 (1995) 6456-6493 [ http://arXiv.org/abs/gr-qc/9504018 ]. - · arXiv
  27. [37][37] M. O. Scully and M. S. Zubairy, Quantum optics . Cambridge University Press, 1997. -
  28. [38][38] T. Thiemann, Complexifier coherent states for quantum general relativity , http://arXiv.org/abs/gr-qc/0206037 . - · arXiv
  29. [42][42] G. Immirzi, Quantum gravity and Regge calculus , Nucl. Phys. Proc. Suppl. 57 (1997) 65-72 [ http://arXiv.org/abs/gr-qc/9701052 ]. - · arXiv
  30. [43][43] J. F. Barbero, Reality conditions and Ashtekar variables: A different perspective , Phys. Rev. D51 (1995) 5498-5506 [ http://arXiv.org/abs/gr-qc/9410013 ]. - · arXiv
  31. [44][44] N. Biggs, Algebraic Graph Theory . Cambridge University Press, Cambridge, 2 ed., 1993. -
  32. [46][46] D. Cvetovic, M. Doob and H. Sachs, Spectra of Graphs . Academic Press, New York, 1979. -
  33. [47][47] M. Gaul and C. Rovelli, A generalized Hamiltonian constraint operator in loop quantum gravity and its simplest Euclidean matrix elements , Class. Quant. Grav. 18 (2001) 1593-1624 [ http://arXiv.org/abs/gr-qc/0011106 ]. - · arXiv
  34. [50][50] T. Thiemann and O. Winkler, Gauge field theory coherent states (GCS). IV: Infinite tensor product and thermodynamical limit , Class. Quant. Grav. 18 (2001) 4997-5054 [ http://arXiv.org/abs/hep-th/0005235 ]. - · arXiv
  35. [53][53] P. Hasenfratz et. al. , The construction of generalized Dirac operators on the lattice , Int. J. Mod. Phys. C12 (2001) 691-708 [ http://arXiv.org/abs/hep-lat/0003013 ]. - · arXiv
  36. [56][56] T. Thiemann, Quantum spin dynamics (QSD). VII: Symplectic structures and continuum lattice formulations of gauge field theories , Class. Quant. Grav. 18 (2001) 3293-3338 [ http://arXiv.org/abs/hep-th/0005232 ]. - · arXiv
  37. [57][57] H. Sahlmann, Coupling Matter to Loop Quantum Gravity . PhD thesis, Universit¨ at Potsdam, 2002. -
  38. [59][59] A. Tanguy, J. P. Wittmer, F. Leonforte and J.-L. Barrat, Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations , http://arXiv.org/abs/cond-mat/0204258 . - · arXiv

Authors
Sahlmann, H., & Thiemann, T.
ORCID
Sahlmann, H
Venue
Classical and Quantum Gravity
Publisher
IOP Publishing
Published
2006-01-19
Volume
23
Issue
3
Pages
867-908
ISSN
  • 0264-9381 (ISSN-L)
  • 1361-6382
DOI
10.1088/0264-9381/23/3/019
OpenAlex
W2041004793
Cited by
84
References
41
Citations by year
2026: 3 · 2025: 2 · 2023: 4 · 2022: 6 · 2021: 3 · 2020: 2 · 2019: 2 · 2018: 1 · 2017: 1 · 2016: 4 · 2015: 2 · 2014: 3 · 2013: 3 · 2012: 8
FWCI
7.06
Type
journal article
Language
en
Open access
Locations
  • Classical and Quantum Gravity (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
Keywords
quantum general relativity, curved spacetime, semiclassical limit, quantum field theory in curved spacetime, background independence, metric operator, coherent states, random lattices, quantum corrections

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review