Real and complex connections for canonical gravity
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Both real and complex connections have been used for canonical gravity: the complex connection has SL(2,C) as the gauge group, while the real connection has SU(2) as the gauge group. We show that there is an arbitrary parameter which enters in the definition of the real connection, in the Poisson brackets, and therefore in the scale of the discrete spectra one finds for areas and volumes in the corresponding quantum theory. A value for could be singled out in the quantum theory by the Hamiltonian constraint or by the rotation to the complex Ashtekar connection.
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Modern LQG and spin foams are based on a relative of Ashtekar's variables known as Ashtekar-Barbero variables.
“Modern LQG and spin foams are based on a certain relative of these variables, that is often referred to as Ashtekar-Barbero variables [56, 227].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [227]
LQG and spin foams are based on the possibility of formulating Hamiltonian general relativity in terms of Yang-Mills-like connection variables.
“LQG and spin foams are based on the possibility of formulating Hamiltonian general relativity in terms of Yang-Mills-like connection variables.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [227]
The case ι = √-1 corresponds to Ashtekar's canonical transformation.
“The case ι = √ -1 corresponds to Ashtekar's canonical transformation [12].”
From Immirzi parameter in quantum general relativity (1998) · cites this paper as [12]
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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
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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
The Spin-Foam Approach to Quantum Gravity
Perez, A. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-3 · Cited by 677 · see citing works
Bojowald, M. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-11 · Cited by 723 · see citing works
Lorentzian spin foam amplitudes: graphical calculus and asymptotics
Barrett, J. W., Dowdall, R. J., Fairbairn, W. J., Hellmann, F., & Pereira, R. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/16/165009 · Cited by 247 · see citing works
EFFECTIVE EQUATIONS OF MOTION FOR QUANTUM SYSTEMS
BOJOWALD, M., & SKIRZEWSKI, A. (2006) · Reviews in Mathematical Physics · doi:10.1142/s0129055x06002772 · Cited by 185 · see citing works
Symmetry reduction for quantized diffeomorphism-invariant theories of connections
Bojowald, M., & Kastrup, H. A. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/15/311 · Cited by 168 · see citing works
HAMILTONIAN ANALYSIS OF GENERAL RELATIVITY WITH THE IMMIRZI PARAMETER
SÁ, N. B. E. (2001) · International Journal of Modern Physics D · doi:10.1142/s0218271801000858 · Cited by 95 · 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
Livine, R. E., & Oriti, D. (2002) · Physical Review D · doi:10.1103/physrevd.65.044025 · Cited by 46 · see citing works
The Quantum Memory Matrix: A Unified Framework for the Black Hole Information Paradox
Neukart, F., Brasher, R., & Marx, E. (2024) · Entropy · doi:10.3390/e26121039 · Cited by 12 · see citing works
- Authors
- Immirzi, G.
- Affiliations
- University of Perugia (IT)
- Corresponding author
- Immirzi, Giorgio
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1997-10-01
- Volume
- 14
- Issue
- 10
- Pages
- L177-L181
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2063176445
- Cited by
- 398
- References
- 1
- Citations by year
- 2026: 19 · 2025: 14 · 2024: 18 · 2023: 17 · 2022: 11 · 2021: 22 · 2020: 11 · 2019: 14 · 2018: 13 · 2017: 21 · 2016: 19 · 2015: 18 · 2014: 15 · 2013: 14 · 2012: 23
- FWCI
- 4.18
- 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
- canonical gravity, SU(2) gauge group, Poisson brackets, quantum gravity, Hamiltonian constraint, Barbero-Immirzi parameter
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