Improved and perfect actions in discrete gravity
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We consider the notion of improved and perfect actions within Regge calculus. These actions are constructed in such a way that they---although being defined on a triangulation---reproduce the continuum dynamics exactly, and therefore capture the gauge symmetries of general relativity. We construct the perfect action in three dimensions with a cosmological constant, and in four dimensions for one simplex. We conclude with a discussion about Regge calculus with curved simplices, which arises naturally in this context.
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In 3D gravity with cosmological constant, the breaking of general covariance by discretization can be shown explicitly at the classical and quantum levels.
“In the simple case of 3D gravity with cosmological constant, this can be shown explicitly at the classical level [45] as well as at the quantum level [304].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [45]
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Asante, S. K., Dittrich, B., & Padua-Argüelles, J. (2023) · Classical and Quantum Gravity · doi:10.1088/1361-6382/accc01 · Cited by 30 · see citing works
Self-citationThe degrees of freedom of area Regge calculus: dynamics, non-metricity, and broken diffeomorphisms
Asante, S. K., Dittrich, B., & Haggard, H. M. (2018) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aac588 · Cited by 29 · see citing works
Self-citationUniversal critical behavior in tensor models for four-dimensional quantum gravity
Eichhorn, A., Lumma, J., Pereira, A. D., & Sikandar, A. (2020) · Journal of High Energy Physics · doi:10.1007/jhep02(2020)110 · Cited by 28 · see citing works
From spin foams to area metric dynamics to gravitons
Dittrich, B., & Kogios, A. (2023) · Classical and Quantum Gravity · doi:10.1088/1361-6382/acc5d9 · Cited by 27 · see citing works
Self-citation4d quantum geometry from 3d supersymmetric gauge theory and holomorphic block
Han, M. (2016) · Journal of High Energy Physics · doi:10.1007/jhep01(2016)065 · Cited by 25 · see citing works
Lorentzian quantum cosmology goes simplicial
Dittrich, B., Gielen, S., & Schander, S. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac42ad · Cited by 24 · see citing works
Self-citationQuantization of systems with temporally varying discretization. II. Local evolution moves
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Vidotto, F. (2011) · Journal of Physics Conference Series · doi:10.1088/1742-6596/314/1/012049 · Cited by 24 · see citing works
Expansions in spin foam cosmology
Hellmann, F. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.103516 · Cited by 23 · see citing works
Towards effective actions for the continuum limit of spin foams
Borissova, J. N., & Dittrich, B. (2023) · Classical and Quantum Gravity · doi:10.1088/1361-6382/accbfb · Cited by 23 · see citing works
Self-citationTurning big bang into big bounce: II. Quantum dynamics
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Discretisations, Constraints and Diffeomorphisms in Quantum Gravity
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Twisted geometries, twistors, and conformal transformations
Långvik, M., & Simone Speziale, D. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.024050 · Cited by 21 · see citing works
Lang, T., Liegener, K., & Thiemann, T. (2018) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aaec3a · Cited by 21 · see citing works
Learning about Quantum Gravity with a Couple of Nodes
Borja, E. F. (2012) · Symmetry Integrability and Geometry Methods and Applications · doi:10.3842/sigma.2012.015 · Cited by 21 · see citing works
Coherent states for quantum gravity: toward collective variables
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Lang, T., Liegener, K., & Thiemann, T. (2018) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aaec54 · Cited by 19 · see citing works
Holonomy spin foam models: boundary Hilbert spaces and time evolution operators
Dittrich, B., Hellmann, F., & Kamiński, W. (2013) · Classical and Quantum Gravity · doi:10.1088/0264-9381/30/8/085005 · Cited by 18 · see citing works
Self-citationTensor Network Renormalization with Fusion Charges—Applications to 3D Lattice Gauge Theory
Cunningham, W. J., Dittrich, B., & Steinhaus, S. (2020) · Universe · doi:10.3390/universe6070097 · Cited by 18 · see citing works
Self-citationTopological lattice field theories from intertwiner dynamicsPreprint
Dittrich, B., & Kamiński, W. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1311.1798 · Cited by 17 · see citing works
Self-citationTowards computational insights into the large-scale structure of spin foamsPreprint
Dittrich, B., & Eckert, F. C. (2012) · Cited by 17 · see citing works
Self-citationFrom 3D topological quantum field theories to 4D models with defects
Delcamp, C., & Dittrich, B. (2017) · Journal of Mathematical Physics · doi:10.1063/1.4989535 · Cited by 16 · see citing works
Self-citationThe Construction of Spin Foam Vertex Amplitudes
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Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity
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Liegener, K., & Singh, P. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.100.124049 · Cited by 14 · see citing works
Renormalization of Group Field Theories for Quantum Gravity: New Computations and Some Suggestions
Finocchiaro, M., & Oriti, D. (2021) · Frontiers in Physics · doi:10.3389/fphy.2020.552354 · Cited by 14 · see citing works
Spin Foams, Refinement Limit, and Renormalization
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Self-citationTowards computational insights into the large-scale structure of spin foams
Dittrich, B., & Eckert, F. C. (2012) · Journal of Physics Conference Series · doi:10.1088/1742-6596/360/1/012004 · Cited by 14 · see citing works
Self-citationSpin Foam Models with Finite GroupsPreprint
Bähr, B., Dittrich, B., & Ryan, J. P. (2011) · arXiv (Cornell University) · doi:10.17863/cam.13547 · Cited by 14 · see citing works
Self-citationde Sitter horizon entropy from a simplicial Lorentzian path integral
Dittrich, B., Ted Jacobson, A., & Padua-Argüelles, J. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.046006 · Cited by 13 · see citing works
Self-citationLorentzian Quantum Cosmology from Effective Spin Foams
Dittrich, B., & Padua-Argüelles, J. (2024) · Universe · doi:10.3390/universe10070296 · Cited by 13 · see citing works
Self-citationOn the space of generalized fluxes for loop quantum gravity
Dittrich, B., Guedes, C., & Oriti, D. (2013) · MPG.PuRe (Max Planck Society) · Cited by 13 · see citing works
Self-citationCarlo Rovelli, C. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1108.0832 · Cited by 13 · see citing works
Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
Bonzom, V. (2012) · Symmetry Integrability and Geometry Methods and Applications · doi:10.3842/sigma.2012.009 · Cited by 12 · see citing works
Holographic description of boundary gravitons in (3+1) dimensions
Asante, S. K., Dittrich, B., & Haggard, H. M. (2019) · Journal of High Energy Physics · doi:10.1007/jhep01(2019)144 · Cited by 12 · see citing works
Self-citationHopf link volume simplicity constraints in spin foam models
Assanioussi, M., & Bahr, B. (2020) · Classical and Quantum Gravity · doi:10.1088/1361-6382/abb117 · Cited by 12 · see citing works
Self-citationCosmological Constant from Condensation of Defect Excitations
Dittrich, B. (2018) · Universe · doi:10.3390/universe4070081 · Cited by 11 · see citing works
Self-citation
- Authors
- Bahr, B., & Dittrich, B.
- Affiliations
- Max Planck Society (DE)
- ORCID
- Dittrich, Bianca
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2009-12-21
- Volume
- 80
- Issue
- 12
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2003786459
- Cited by
- 138
- References
- 62
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 5 · 2023: 8 · 2022: 4 · 2021: 8 · 2020: 7 · 2019: 6 · 2018: 8 · 2017: 6 · 2016: 13 · 2015: 9 · 2014: 12 · 2013: 17 · 2012: 16
- FWCI
- 7.57
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- Max Planck Institute for Plasma Physics (submittedVersion)
- Max Planck Digital Library (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- European Commission
- 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
- Regge calculus, improved actions, perfect action, discrete gravity, triangulation, gauge invariance, general relativity, cosmological constant, simplicial quantum gravity
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