Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation
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The present paper is the companion of Sahlmann and Thiemann ( 2006 Towards the QFT on curved spacetime limit of QGR: I. A general scheme Class. Quantum Grav. 23 867 ) in which we proposed a scheme that tries to derive the quantum field theory (QFT) on curved spacetimes (CST) limit from background-independent quantum general relativity (QGR). The constructions of the companion paper make heavy use of the notion of semiclassical states for QGR . In the present paper, we employ the complexifier coherent states for QGR recently proposed by Thiemann and Winkler as semiclassical states, and thus fill the general formulae obtained in the companion paper with life. We demonstrate how one can, under some simplifying assumptions, explicitly compute expectation values of the operators relevant for the gravity–matter Hamiltonians of the companion paper in the complexifier coherent states. These expectation values give rise to effective matter Hamiltonians on the background on which the gravitational coherent state is peaked and thus induce approximate notions of n -particle states and matter propagation on fluctuating spacetimes. We display the details for the scalar and the electromagnetic field. The effective theories exhibit two types of corrections as compared to the ordinary QFT on CST. The first is due to the quantum fluctuations of the gravitational field and the second arises from the fact that background independence forces both geometry and matter to propagate on a spacetime of the form , where γ is a (random) graph. Finally, we obtain explicit numerical predictions for non-standard dispersion relations for the scalar and the electromagnetic field. They should, however, not be taken too seriously, due to the many ambiguities in our scheme, the analysis of the physical significance of which has only begun. We show, however, that one can classify these ambiguities at least in broad terms.
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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 [341]
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References 29 · Cited by 114
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- Sahlmann H and Thiemann T 2006 Towards the QFT on curved spacetime limit of QGR: I. A general scheme Class. Quantum Grav. 23 867 (Preprint gr-qc/0207030) · arXiv
- Rovelli C 1998 Loop quantum gravity Living Rev. Rel. 1 1 (Preprint gr-qc/9710008) · arXiv
- Rovelli C 2000 The century of the incomplete revolution: searching for general relativistic quantum field theory J. Math. Phys. 41 3776-800 (Preprint hep-th/9910131) · DOI
- Ashtekar A, Rovelli C and Smolin L 1992 Weaving a classical geometry with quantum threads Phys. Rev. Lett. 69 237-40 (Preprint hep-th/9203079) · DOI · Paper page
- Bombelli L 2001 Statistical geometry of random weave states Preprint gr-qc/0101080 · arXiv
- Thiemann T 2001 Gauge field theory coherent states (GCS): I. General properties Class. Quantum Grav. 18 2025-64 (Preprint hep-th/0005233) · DOI
- Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): II. Peakedness properties Class. Quantum Grav. 18 2561-636 (Preprint hep-th/0005237) · DOI
- Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): III. Ehrenfest theorems Class. Quantum Grav. 18 4629-82 (Preprint hep-th/0005234) · DOI
- Iwasaki J and Rovelli C 1994 Gravitons from loops: nonperturbative loop space quantum gravity contains the graviton physics approximation Class. Quantum Grav. 11 1653-76 · DOI · Paper page
- Ashtekar A, Rovelli C and Smolin L 1991 Gravitons and loops Phys. Rev. D 44 1740-55 (Preprint hep-th/9202054) · DOI
- Varadarajan M 2002 Gravitons from a loop representation of linearized gravity Preprint gr-qc/0204067 · arXiv
- Varadarajan M 2001 Photons from quantized electric flux representations Phys. Rev. D 64 104003 (Preprint gr-qc/0104051) · DOI
- Varadarajan M 2000 Fock representations from U(1) holonomy algebras Phys. Rev. D 61 104001 (Preprint gr-qc/0001050) · DOI
- Ashtekar A and Lewandowski J 2001 Relation between polymer and Fock excitations Class. Quantum Grav. 18 L117-28 (Preprint gr-qc/0107043) · DOI
- Sahlmann H, Thiemann T and Winkler O 2001 Coherent states for canonical quantum general relativity and the infinite tensor product extension Nucl. Phys. B 606 401-40 (Preprint gr-qc/0102038) · DOI
- Thiemann T 2002 Complexifier coherent states for quantum general relativity Preprint gr-qc/0206037 · arXiv
- Rovelli C 1991 What is observable in classical and quantum gravity? Class. Quantum Grav. 8 297-316 · DOI · Paper page
- Rovelli C 1991 Quantum reference systems Class. Quantum Grav. 8 317-32 · DOI · Paper page
- Thiemann T 1998 QSD: V. Quantum gravity as the natural regulator of matter quantum field theories Class. Quantum Grav. 15 1281-314 (Preprint gr-qc/9705019) · DOI · Paper page
- Alfaro J, Morales-Tecotl H A and Urrutia L F 2000 Quantum gravity corrections to neutrino propagation Phys. Rev. Lett. 84 2318-21 (Preprint gr-qc/9909079) · DOI
- Alfaro J, Morales-Tecotl H A and Urrutia L F 2001 Loop quantum gravity and light propagation Preprint hep-th/0108061 · arXiv
- Alfaro J and Palma G 2001 Loop quantum gravity corrections and cosmic rays decays Preprint hep-th/0111176 · arXiv
- Christ N H, Friedberg R and Lee T D 1982 Random lattice field theory: general formulation Nucl. Phys. B 202 89 · DOI
- Christ N H, Friedberg R and Lee T D 1982 Gauge theory on a random lattice Nucl. Phys. B 210 310 · DOI
- Christ N H, Friedberg R and Lee T D 1982 Weights of links and plaquettes in a random lattice Nucl. Phys. B 210 337 · DOI
- Tanguy A, Wittmer J P, Leonforte F and Barrat J-L 2002 Continuum limit of amorphous elastic bodies: a finite-size study of low frequency harmonic vibrations Preprint cond-mat/0204258 · arXiv
- Hall B 1994 The Segal-Bargmann 'coherent state' transform for compact Lie groups J. Funct. Anal. 122 103-51 · DOI
- Hall B 1997 Phase space bounds for quantum mechanics on a compact Lie group Commun. Math. Phys. 184 233-50 · DOI
- Thiemann T 2001 Quantum spin dynamics (QSD): VII. Symplectic structures and continuum lattice formulations of gauge field theories Class. Quantum Grav. 18 3293-338 (Preprint hep-th/0005232) · DOI
- Ashtekar A and Lewandowski J 1998 Quantum theory of geometry: II. Volume operators Adv. Theor. Math. Phys. 1 388 (Preprint gr-qc/9711031) · arXiv
- Ashcroft N W and Mermin N 1976 Solid State Physics (London: Harcourt Brace) chapter 22
- Authors
- Sahlmann, H., & Thiemann, T.
- Affiliations
- Max Planck Institute for Gravitational Physics (DE)
- ORCID
- Sahlmann, H
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2006-01-19
- Volume
- 23
- Issue
- 3
- Pages
- 909-954
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W1991845639
- Cited by
- 114
- References
- 29
- Citations by year
- 2026: 1 · 2024: 2 · 2023: 4 · 2022: 7 · 2021: 2 · 2019: 4 · 2018: 2 · 2017: 1 · 2016: 7 · 2015: 2 · 2014: 4 · 2013: 2 · 2012: 9
- FWCI
- 8.61
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (0090091)
- Pennsylvania State University
- Studienstiftung des Deutschen Volkes
- 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 field theory in curved spacetime, background-independent quantum gravity, semiclassical states, quantum fluctuations of spacetime, random graphs, modified dispersion relations, scalar field, electromagnetic fields, matter-gravity coupling
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