Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory
Abstract
Quantum gravity is among the most fascinating problems in physics. It modifies our understanding of time, space and matter. The recent development of the loop approach has allowed us to explore domains ranging from black hole thermodynamics to the early Universe. This book provides readers with a simple introduction to loop quantum gravity, centred on its covariant approach. It focuses on the physical and conceptual aspects of the problem and includes the background material needed to enter this lively domain of research, making it ideal for researchers and graduate students. Topics covered include quanta of space; classical and quantum physics without time; tetrad formalism; Holst action; lattice QCD; Regge calculus; ADM and Ashtekar variables; Ponzano-Regge and Turaev-Viro amplitudes; kinematics and dynamics of 4D Lorentzian quantum gravity; spectrum of area and volume; coherent states; classical limit; matter couplings; graviton propagator; spinfoam cosmology and black hole thermodynamics.
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A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb01338.x · Cited by 88,486 · see citing works
Particle creation by black holes
Hawking, S. W. (1975) · Communications In Mathematical Physics · doi:10.1007/bf02345020 · Cited by 13,106 · see citing works
HAWKING, S. W. (1974) · Nature · doi:10.1038/248030a0 · Cited by 5,669 · see citing works
Zur Elektrodynamik bewegter Körper
Einstein, A. (1905) · Annalen der Physik · doi:10.1002/andp.19053221004 · Cited by 4,385 · see citing works
Role of Conformal Three-Geometry in the Dynamics of Gravitation
York, J. W. (1972) · Physical Review Letters · doi:10.1103/physrevlett.28.1082 · Cited by 1,392 · 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
Self-citationQuantum 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
Lectures on Non-Perturbative Canonical Gravity
Ashtekar, A. (1991) · Advanced Series in Astrophysics and Cosmology · doi:10.1142/1321 · Cited by 872 · 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
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
LQG vertex with finite Immirzi parameter
Engle, J., Livine, E., Pereira, R., & Rovelli, C. (2008) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2008.02.018 · Cited by 584 · see citing works
TOPOLOGICAL LATTICE MODELS IN FOUR DIMENSIONS
OOGURI, H. (1992) · Modern Physics Letters A · doi:10.1142/s0217732392004171 · Cited by 379 · see citing works
Loop-Quantum-Gravity Vertex Amplitude
Engle, J., Pereira, R., & Rovelli, C. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.161301 · Cited by 335 · see citing works
A MODEL OF THREE-DIMENSIONAL LATTICE GRAVITY
BOULATOV, D. V. (1992) · Modern Physics Letters A · doi:10.1142/s0217732392001324 · Cited by 326 · 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
Spin-foams for all loop quantum gravity
Kamiński, W., Kisielowski, M., & Lewandowski, J. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/9/095006 · Cited by 191 · see citing works
Complete LQG propagator: Difficulties with the Barrett-Crane vertex
Alesci, E., & Rovelli, C. (2007) · Physical Review D · doi:10.1103/physrevd.76.104012 · Cited by 154 · see citing works
LQG propagator from the new spin foams
Bianchi, E., Magliaro, E., & Perini, C. (2009) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2009.07.016 · Cited by 126 · see citing works
Quantum-reduced loop gravity: Cosmology
Alesci, E., & Cianfrani, F. (2013) · Physical Review D · doi:10.1103/physrevd.87.083521 · Cited by 90 · see citing works
Bahr, B., Hellmann, F., Kamiński, W., Kisielowski, M., & Lewandowski, J. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/10/105003 · Cited by 63 · see citing works
Regularization and finiteness of the Lorentzian loop quantum gravity vertices
Engle, J., & Pereira, R. (2009) · Physical Review D · doi:10.1103/physrevd.79.084034 · Cited by 63 · see citing works
New vertices and canonical quantization
Alexandrov, S. (2010) · Physical Review D · doi:10.1103/physrevd.82.024024 · Cited by 48 · see citing works
The EPRL intertwiners and corrected partition function
Kamiński, W., Kisielowski, M., & Lewandowski, J. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/16/165020 · Cited by 43 · see citing works
The physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
Ding, Y., & Rovelli, C. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/20/205003 · Cited by 42 · see citing works
TOPOLOGICAL MEASURE AND GRAPH-DIFFERENTIAL GEOMETRY ON THE QUOTIENT SPACE OF CONNECTIONS
LEWANDOWSKI, J. (1994) · International Journal of Modern Physics D · doi:10.1142/s0218271894000307 · Cited by 36 · see citing works
The Euclidean three-point function in loop and perturbative gravity
Rovelli, C., & Zhang, M. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/17/175010 · Cited by 31 · see citing works
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de Cesare, M., Pithis, A. G. A., & Sakellariadou, M. (2016) · Physical Review D · doi:10.1103/physrevd.94.064051 · Cited by 72 · see citing works
Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free
Bianconi, G., & Rahmede, C. (2015) · Scientific Reports · doi:10.1038/srep13979 · Cited by 61 · see citing works
Impact of nonlinear effective interactions on group field theory quantum gravity condensates
Pithis, A. G. A., Sakellariadou, M., & Tomov, P. (2016) · Physical Review D · doi:10.1103/physrevd.94.064056 · Cited by 34 · see citing works
Li, Y., Han, M., Grassl, M., & Zeng, B. (2017) · New Journal of Physics · doi:10.1088/1367-2630/aa7235 · Cited by 15 · see citing works
- Authors
- Rovelli, C., & Vidotto, F.
- Affiliations
- Radboud University Nijmegen (NL)
- ORCID
- Vidotto, Francesca
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 2014-11-13
- OpenAlex
- W1931954910
- Cited by
- 544
- References
- 26
- Citations by year
- 2026: 37 · 2025: 80 · 2024: 49 · 2023: 35 · 2022: 51 · 2021: 45 · 2020: 41 · 2019: 56 · 2018: 51 · 2017: 38 · 2016: 36 · 2015: 19 · 2014: 4 · 2013: 1
- FWCI
- 10.54
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Cambridge University Press eBooks (publishedVersion)
- 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, tetrad formalism, Holst action, Regge calculus, lattice QCD, Ashtekar variables, coherent states, classical limit, matter coupling, graviton propagator, black hole thermodynamics, Lorentzian quantum gravity
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