Is Barbero's Hamiltonian formulation a gauge theory of Lorentzian gravity?
Open accessAbstract
This letter is a critique of Barbero's constrained Hamiltonian formulation of general relativity, on which current work in loop quantum gravity is based. While we do not dispute the correctness of Barbero's formulation of general relativity, we offer some criticisms of an aesthetic nature. We point out that unlike Ashtekar's complex SU (2) connection, Barbero's real SO (3) connection does not admit an interpretation as a space-time gauge field. We show that if one tries to interpret Barbero's real SO (3) connection as a space-time gauge field, the theory is not diffeomorphism invariant. We conclude that Barbero's formulation is not a gauge theory of gravity in the sense that Ashtekar's Hamiltonian formulation is. The advantages of Barbero's real connection formulation have been bought at the price of giving up the description of gravity as a gauge field.
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.
Integrity signals
Registry
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.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
2 + 1 dimensional gravity as an exactly soluble system
Witten, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90143-5 · Cited by 2,562 · see citing works
Quantum geometry and black hole entropy
Ashtekar, A., Baez, J., Corichi, A., & Krasnov, K. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.904 · Cited by 1,105 · see citing works
Logarithmic correction to the Bekenstein-Hawking entropyPreprint
Kaul, R. K., & Majumdar, P. (2000) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0002040
Flagged first, then by citations
Research works printed but not linked: 11
- For exhaustive references in this area, see the review article by Gaul M and Rovelli C Preprint gr-qc/9910079 · arXiv
- Carlip S 1998 Quantum Gravity in 2 + 1 Dimensions (Cambridge: Cambridge University Press)
- Barbero J F 1995 Phys. Rev. D 51 5507 (Barbero J F 1995 Preprint gr-qc/9410014) · arXiv
- See Rovelli C 1997 Loop Quantum Gravity Living Reviews Preprint gr-qc/9710008 · arXiv
- Immirzi G 1997 Class. Quantum Grav. 14 L177-81 (Immirzi G 1995 Preprint gr-qc/9511026) · arXiv
- Holst S 1996 Phys. Rev. D 53 5966 (Holst S 1995 Preprint gr-qc/9511026) · arXiv
- Ashtekar A 1991 (notes prepared in collaboration with R Tate) Lectures on Non-perturbative Canonical Gravity (Singapore: World Scientific)
- Samuel J 2000 Canonical Gravity, Diffeomorphisms and Objective Histories Preprint
- Alexandrov S 2000 SO(4, C)-covariant Ashtekar-Barbero gravity and the Immirzi parameter Preprint gr-qc/0005085 · arXiv
- Barros e Sá N 2000 Hamiltonian analysis of general relativity with the Immirzi parameter Preprint gr-qc/0006013 · arXiv
- Rovelli C and Thiemann T 1997 The Immirzi parameter in quantum general relativity Preprint gr-qc/9705059 · arXiv
Cited by
Sorted by citations
Background independent quantum gravity: a status report
Ashtekar, A., & Lewandowski, J. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/15/r01 · Cited by 1,951 · see citing works
Alexandrov, S., & Livine, E. R. (2003) · Physical Review D · doi:10.1103/physrevd.67.044009 · Cited by 141 · see citing works
Choice of connection in loop quantum gravity
Alexandrov, S. (2001) · Physical Review D · doi:10.1103/physrevd.65.024011 · Cited by 80 · see citing works
Area spectrum in Lorentz covariant loop gravity
Alexandrov, S., & Vassilevich, D. (2001) · Physical Review D · doi:10.1103/physrevd.64.044023 · Cited by 68 · 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
Self-citation
- Authors
- Samuel, J.
- Affiliations
- Raman Research Institute (IN)
- Corresponding author
- Samuel, Joseph
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2000-09-26
- Volume
- 17
- Issue
- 20
- Pages
- L141-L148
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2015547845
- Cited by
- 83
- References
- 3
- Citations by year
- 2024: 3 · 2023: 1 · 2022: 1 · 2021: 4 · 2020: 2 · 2019: 1 · 2018: 2 · 2017: 5 · 2016: 7 · 2015: 8 · 2014: 6 · 2013: 4 · 2012: 3
- FWCI
- 2.71
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- 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
- general relativity, loop quantum gravity, SU(2) connection, gauge theory of gravity, diffeomorphism invariance
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
