Quantization of Chern-Simons gauge theory with complex gauge group
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For noncompact groups such as those appearing in gravity, much less is known, though there has been promising work.
“For noncompact groups such as those that appear in gravity, much less is known, though there has been some promising work [280, 155, 43, 150].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [280]
For Λ > 0, the relevant gauge group is SO(3,1) or its cover SL(2,C), a complex gauge group whose Chern-Simons theory is somewhat better understood.
“For Λ > 0, the relevant gauge group is SO(3, 1) or its cover SL(2, ℂ), a complex gauge group whose Chern-Simons theory is somewhat better understood [280, 155, 43].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [280]
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
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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
- Witten, E.
- Affiliations
- Institute for Advanced Study (US)
- Corresponding author
- Witten, Edward
- ORCID
- Witten, Edward
- Venue
- Communications in Mathematical Physics
- Published
- 1991-03
- Volume
- 137
- Issue
- 1
- Pages
- 29-66
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W2019068283
- Cited by
- 269
- References
- 1
- Citations by year
- 2026: 7 · 2025: 23 · 2024: 10 · 2023: 17 · 2022: 9 · 2021: 9 · 2020: 10 · 2019: 11 · 2018: 9 · 2017: 13 · 2016: 12 · 2015: 13 · 2014: 9 · 2013: 9 · 2012: 2
- FWCI
- 4.41
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Communications in Mathematical Physics (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- Chern-Simons theory, canonical quantization, three-dimensional gravity, SL(2,C), Lorentz signature, positive cosmological constant, Euclidean signature, negative cosmological constant, central charge, conformal field theory, conformal blocks, infinite-dimensional Hilbert spaces
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