Area spectrum in Lorentz covariant loop gravity
Open accessAbstract
We use the manifestly Lorentz covariant canonical formalism to evaluate eigenvalues of the area operator acting on Wilson lines. To this end we modify the standard definition of the loop states to make it applicable to the present case of noncommutative connections. The area operator is diagonalized by using the usual shift ambiguity in the definition of the connection. The eigenvalues are then expressed through quadratic Casimir operators. No dependence on the Immirzi parameter appears.
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Cites
Basdevant, J.-L. (2007) · Springer eBooks · doi:10.1007/978-0-387-37748-3 · Cited by 2,873 · see citing works
Discreteness of area and volume in quantum gravity
Rovelli, C., & Smolin, L. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00150-q · Cited by 1,365 · see citing works
Quantum theory of geometry: I. Area operators
Ashtekar, A., & Lewandowski, J. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/1a/006 · Cited by 852 · see citing works
Loop space representation of quantum general relativity
Rovelli, C., & Smolin, L. (1990) · Nuclear Physics B · doi:10.1016/0550-3213(90)90019-a · Cited by 806 · see citing works
Real Ashtekar variables for Lorentzian signature space-times
Barbero G., J. F. (1995) · Physical Review D · doi:10.1103/physrevd.51.5507 · Cited by 758 · see citing works
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/4/011 · Cited by 750 · see citing works
Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
Holst, S. (1996) · Physical Review D · doi:10.1103/physrevd.53.5966 · Cited by 576 · see citing works
An Introduction to Spin Foam Models of BF Theory and Quantum Gravity
Baez, J. C. (2000) · Lecture Notes in Physics · doi:10.1007/3-540-46552-9_2 · Cited by 464 · see citing works
Knot Theory and Quantum Gravity
Rovelli, C., & Smolin, L. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.1155 · Cited by 463 · see citing works
Projective techniques and functional integration for gauge theories
Ashtekar, A., & Lewandowski, J. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531037 · Cited by 388 · see citing works
Baez, J. C. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/7/004 · Cited by 381 · see citing works
“Sum over surfaces” form of loop quantum gravity
Reisenberger, M. P., & Rovelli, C. (1997) · Physical Review D · doi:10.1103/physrevd.56.3490 · Cited by 372 · see citing works
Englert, B. (2006) · WORLD SCIENTIFIC eBooks · doi:10.1142/6093-vol1 · Cited by 351 · see citing works
Representations of the holonomy algebras of gravity and nonAbelian gauge theories
Ashtekar, A., & Isham, C. J. (1992) · Classical and Quantum Gravity · doi:10.1088/0264-9381/9/6/004 · Cited by 310 · see citing works
Differential geometry on the space of connections via graphs and projective limits
Ashtekar, A., & Lewandowski, J. (1995) · Journal of Geometry and Physics · doi:10.1016/0393-0440(95)00028-g · Cited by 303 · see citing works
Quantum gravity and Regge calculus
Immirzi, G. (1997) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(97)00354-x · Cited by 287 · see citing works
Quantum spin dynamics (QSD): II. The kernel of the Wheeler - DeWitt constraint operator
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/4/012 · Cited by 247 · see citing works
Geometry eigenvalues and the scalar product from recoupling theory in loop quantum gravity
De Pietri, R., & Rovelli, C. (1996) · Physical Review D · doi:10.1103/physrevd.54.2664 · Cited by 201 · see citing works
Immirzi parameter in quantum general relativity
Rovelli, C., & Thiemann, T. (1998) · Physical Review D · doi:10.1103/physrevd.57.1009 · Cited by 171 · see citing works
Volume Operator in Discretized Quantum Gravity
Loll, R. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.3048 · Cited by 124 · see citing works
<i>SO</i> (4, <i>C</i> )-covariant Ashtekar-Barbero gravity and the Immirzi parameter
Alexandrov, S. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/20/307 · Cited by 112 · see citing works
Self-citationLewandowski, J. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/1/010 · Cited by 112 · see citing works
Spin foam model for Lorentzian general relativity
Pérez, A., & Carlo Rovelli, C. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.63.041501 · Cited by 102 · see citing works
Reality conditions and Ashtekar variables: A different perspective
G., J. F. B. (1995) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.51.5498 · Cited by 95 · see citing works
The complete spectrum of the area from recoupling theory in loop quantum gravity
Frittelli, S., Lehner, L., & Rovelli, C. (1996) · Classical and Quantum Gravity · doi:10.1088/0264-9381/13/11/008 · Cited by 95 · see citing works
Exact path integral quantization of generic 2D dilaton gravity
Kummer, W., Liebl, H., & Vassilevich, D. (1997) · Nuclear Physics B · doi:10.1016/s0550-3213(97)00143-0 · Cited by 94 · see citing works
Self-citationSpectrum of the volume operator in quantum gravity
Loll, R. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(95)00627-3 · Cited by 90 · see citing works
Is Barbero's Hamiltonian formulation a gauge theory of Lorentzian gravity?
Samuel, J. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/20/101 · Cited by 83 · see citing works
From Euclidean to Lorentzian general relativity: The real way
G., J. F. B. (1996) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.54.1492 · Cited by 65 · see citing works
Real-polynomial formulation of general relativity in terms of connections
G., J. F. B. (1994) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.49.6935 · Cited by 64 · see citing works
BF gravity and the Immirzi parameter
Capovilla, R., Montesinos, M., Prieto, V. A., & Rojas, E. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/5/101 · Cited by 55 · see citing works
Non-perturbative solutions for lattice quantum gravity
Loll, R. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00184-t · Cited by 47 · see citing works
Integrating geometry in general 2D dilaton gravity with matter
Kummer, W., Liebl, H., & Vassilevich, D. V. (1999) · Nuclear Physics B · doi:10.1016/s0550-3213(99)00047-4 · Cited by 41 · see citing works
Self-citationPath integral for the Hilbert-Palatini and Ashtekar gravity
Alexandrov, S. Y., & Vassilevich, D. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.58.124029 · Cited by 33 · see citing works
Self-citationLoop Quantum Gravity and the Meaning of Diffeomorphism InvariancePreprint
Gaul, M., & Rovelli, C. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9910079 · Cited by 32 · see citing works
The virtual black hole in 2d quantum gravity
Grumiller, D., Kummer, W., & Vassilevich, D. V. (2000) · Nuclear Physics B · doi:10.1016/s0550-3213(00)00231-5 · Cited by 32 · see citing works
Self-citationNon-perturbative path integral of 2d dilaton gravity and two-loop effects from scalar matter
Kummer, W., Liebl, H., & Vassilevich, D. (1998) · Nuclear Physics B · doi:10.1016/s0550-3213(97)00796-7 · Cited by 26 · see citing works
Self-citationBF gravity and the Immirzi parameter
Capovilla, R., Montesinos, M., Prieto, V. A., & Rojas, E. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/6/501 · Cited by 16 · see citing works
Comment on Holst’s Lagrangian formulation
Samuel, J. (2001) · Physical Review D · doi:10.1103/physrevd.63.068501 · Cited by 11 · see citing works
Immirzi parameter in the Barrett-Crane model?Preprint
Livine, R. E. (2001) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0103081 · Cited by 6 · see citing works
A 2-SURFACE QUANTIZATION OF THE LORENTZIAN GRAVITY
Bobieński, M., Lewandowski, J., & Mroczek, M. (2002) · The Ninth Marcel Grossmann Meeting · doi:10.1142/9789812777386_0215 · Cited by 5 · see citing works
Flagged first, then by citations
Research works printed but not linked: 10
- [4][4] C. Rovelli and L. Smolin, Nucl. Phys. B442 , 593 (1995); J. Lewandowski, The operators of quantum gravity lecture at the workshop on canonical and quantum gravity (Warsaw, 1995); S. Frittelli, L. Lehner, and C. Rovelli, Class Quantum Grav. 13 , 2921 (1996). -
- [7][7] G. Immirzi, Nucl. Phys. Proc. Suppl. 57 , 65 (1997) [gr-qc/9701052]. - · arXiv
- [10][10] S. Alexandrov, Class. Quantum Grav. 17 , 4255 (2000) [gr-qc/0005085]. - · arXiv
- [11][11] S. Yu. Alexandrov and D. V. Vassilevich, Phys. Rev. D 58 , 124029 (1998) [gr-qc/9806001]. - · arXiv
- [12][12] W. Kummer, H. Liebl and D. V. Vassilevich, Nucl. Phys. B 493 , 491 (1997) [grqc/9612012]; Nucl. Phys. B 513 , 723 (1998) [hep-th/9707115]; Nucl. Phys. B 544 , 403 (1999) [hep-th/9809168]; D. Grumiller, W. Kummer and D. V. Vassilevich, Nucl. Phys. B 580 , 438 (2000) [gr-qc/0001038]. - · arXiv
- [13][13] J. Samuel, Class. Quantum Grav. 17 , L141 (2000) [gr-qc/0005095]; Phys. Rev. D 63 , 068501 (2001). - · arXiv
- [14][14] A. Perez and C. Rovelli, Phys. Rev. D 63 , 041501 (2001) [gr-qc/0009021]; 3+1 spinfoam model of quantum gravity with spacelike and timelike components, gr-qc/0011037. - · arXiv
- [15][15] J. Baez, Class. Quantum Grav. 15 , 1827 (1998) [gr-qc/9709052]; Lect. Notes Phys. 543 , 25 (2000) [gr-qc/9905087]; M. Reisenberger and C. Rovelli, Phys. Rev. D 56 , 3490 (1997) [gr-qc/9612035]. - · arXiv
- [18][18] T. Thiemann, Class. Qauntum Grav. 15 , 839 (1998) [gr-qc/9606089]; Class. Qauntum Grav. 15 , 875 (1998) [gr-qc/9606090]. - · arXiv
- [20][20] R. Capovilla, M. Montesinos, V.A. Prieto and E. Rojas, Class. Quantum Grav. 18 , 49 (2001) [gr-qc/0102073]. - · arXiv
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- Authors
- Alexandrov, S., & Vassilevich, D.
- Affiliations
- St Petersburg University (RU)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2001-07-30
- Volume
- 64
- Issue
- 4
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2163053643
- Cited by
- 68
- References
- 40
- Citations by year
- 2025: 1 · 2022: 1 · 2021: 1 · 2020: 1 · 2019: 2 · 2018: 3 · 2017: 6 · 2016: 4 · 2015: 3 · 2014: 1 · 2013: 2 · 2012: 5
- FWCI
- 3.27
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Deutsche Forschungsgemeinschaft
- 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
- loop quantum gravity, Lorentz covariance, area operator, Wilson lines, quadratic Casimir operator, Immirzi parameter, eigenvalues
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 ›
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