On the relation between 2+1 Einstein gravity and Chern-Simons theory
Open accessAbstract
A simple example is given to show that the gauge equivalence classes of physical states in Chern-Simons theory are not in one-to-one correspondence with those of Einstein gravity in three spacetime dimensions. The two theories are therefore not equivalent. It is shown that including singular metrics into general relativity has more, and in fact a quite counter-intuitive, impact on the theory than one naively expects.
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.
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?
A similar ambiguity occurs for 2+1 gravity with point particles, which may imply a physical difference between the metric and Chern-Simons formulations.
“A similar ambiguity occurs for (2 + 1)-dimensional gravity with point particles, where, as Matschull has emphasized [194], it may imply a physical difference between the metric and Chern-Simons formulations of (2 + 1)-dimensional gravity.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [194]
If the invertibility condition for e is dropped, the first-order formalism is no longer quite equivalent to the metric formalism.
“The invertibility condition for e is important; if it is dropped, the first-order formalism is no longer quite equivalent to the metric formalism [194].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [194]
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
Flagged first, then by citations
Cited by
Sorted by citations
Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
- Authors
- Matschull, H.-J.
- Affiliations
- Johannes Gutenberg University Mainz (DE)
- Corresponding author
- Matschull, Hans-Jürgen
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1999-07-20
- Volume
- 16
- Issue
- 8
- Pages
- 2599-2609
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2045246764
- Cited by
- 86
- References
- 1
- Citations by year
- 2023: 2 · 2022: 3 · 2021: 4 · 2020: 5 · 2019: 5 · 2018: 4 · 2017: 2 · 2016: 2 · 2015: 3 · 2014: 2 · 2013: 1 · 2012: 6
- FWCI
- 4.40
- 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)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- Chern-Simons theory, gauge equivalence, 2+1 dimensions, singular metrics, equivalence of theories, physical states
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
