Path integral measure and triangulation independence in discrete gravity
Open accessAbstract
A path integral measure for gravity should also preserve the fundamental symmetry of general relativity, which is diffeomorphism symmetry. In previous work, we argued that a successful implementation of this symmetry into discrete quantum gravity models would imply discretization independence. We therefore consider the requirement of triangulation independence for the measure in (linearized) Regge calculus, which is a discrete model for quantum gravity, appearing in the semi--classical limit of spin foam models. To this end we develop a technique to evaluate the linearized Regge action associated to Pachner moves in 3D and 4D and show that it has a simple, factorized structure. We succeed in finding a local measure for 3D (linearized) Regge calculus that leads to triangulation independence. This measure factor coincides with the asymptotics of the Ponzano Regge Model, a 3D spin foam model for gravity. We furthermore discuss to which extent one can find a triangulation independent measure for 4D Regge calculus and how such a measure would be related to a quantum model for 4D flat space. To this end, we also determine the dependence of classical Regge calculus on the choice of triangulation in 3D and 4D.
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Even linearized classical Regge calculus in four dimensions is not discretization independent.
“Even linearized classical Regge calculus is not discretization independent in 4D as shown in [152], where a general discussion of the issues raised in this section are considered.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [152]
Cites
Quantum Theory of Gravity. I. The Canonical Theory
DeWitt, B. S. (1967) · Physical Review · doi:10.1103/physrev.160.1113 · Cited by 3,385 · see citing works
General relativity without coordinates
Regge, T. (1961) · Il Nuovo Cimento · doi:10.1007/bf02733251 · Cited by 1,477 · see citing works
State sum invariants of 3-manifolds and quantum 6j-symbols
Turaev, V. G., & Viro, O. Y. (1992) · Topology · doi:10.1016/0040-9383(92)90015-a · Cited by 1,145 · see citing works
Christensen, S. M. (1984) · Cited by 1,059 · 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
Path integrals and the indefiniteness of the gravitational action
Gibbons, G. W., Hawking, S. W., & Perry, M. J. (1978) · Nuclear Physics B · doi:10.1016/0550-3213(78)90161-x · Cited by 669 · see citing works
Spin foam models for quantum gravity
Perez, A. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/6/202 · Cited by 532 · see citing works
Group Field Theory: An Overview
Freidel, L. (2005) · International Journal of Theoretical Physics · doi:10.1007/s10773-005-8894-1 · Cited by 378 · see citing works
P.L. Homeomorphic Manifolds are Equivalent by Elementary 5hellingst
Pachner, U. (1991) · European Journal of Combinatorics · doi:10.1016/s0195-6698(13)80080-7 · Cited by 351 · see citing works
Colored Tensor Models - a Review
Gurău, R. (2012) · Symmetry Integrability and Geometry Methods and Applications · doi:10.3842/sigma.2012.020 · Cited by 324 · see citing works
SEMICLASSICAL LIMIT OF RACAH COEFFICIENTS.
Ponzano, G., & Regge, T. (1969) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · Cited by 315 · see citing works
Twisted geometries: A geometric parametrization of SU(2) phase space
Freidel, L., & Simone Speziale, D. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.084040 · Cited by 258 · see citing works
Group Field Theory: An overview
Freidel, L. (2005) · CERN Document Server (European Organization for Nuclear Research) · Cited by 249 · see citing works
Discrete Approaches to Quantum Gravity in Four Dimensions
Loll, R. (1998) · Living Reviews in Relativity · doi:10.12942/lrr-1998-13 · Cited by 232 · see citing works
Feynman Quantization of General Relativity
Misner, C. W. (1957) · Reviews of Modern Physics · doi:10.1103/revmodphys.29.497 · Cited by 231 · see citing works
Asymptotic analysis of the Engle–Pereira–Rovelli–Livine four-simplex amplitude
Barrett, J. W., Dowdall, R. J., Fairbairn, W. J., Gomes, H., & Hellmann, F. (2009) · Journal of Mathematical Physics · doi:10.1063/1.3244218 · Cited by 224 · see citing works
Rocek, M., & Williams, R. M. (1981) · Physics Letters B · doi:10.1016/0370-2693(81)90848-0 · Cited by 217 · see citing works
Semiclassical limit of 4-dimensional spin foam models
Conrady, F., & Freidel, L. (2008) · Physical Review D · doi:10.1103/physrevd.78.104023 · Cited by 213 · see citing works
Four-dimensional simplicial quantum gravity
Ambjørn, J., & Jurkiewicz, J. (1992) · Physics Letters B · doi:10.1016/0370-2693(92)90709-d · Cited by 205 · 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
The group field theory approach to Quantum Gravity
Oriti, D. (2009) · Cambridge University Press eBooks · doi:10.1017/cbo9780511575549.020 · Cited by 186 · see citing works
The quantization of Regge calculus
Rocek, M., & Williams, R. M. (1984) · The European Physical Journal C · doi:10.1007/bf01581603 · Cited by 181 · see citing works
Diffeomorphisms and spin foam models
Freidel, L., & Louapre, D. (2003) · Nuclear Physics B · doi:10.1016/s0550-3213(03)00306-7 · Cited by 155 · see citing works
Area–angle variables for general relativity
Dittrich, B., & Simone Speziale, D. (2008) · New Journal of Physics · doi:10.1088/1367-2630/10/8/083006 · Cited by 147 · see citing works
Self-citationPhase space descriptions for simplicial 4D geometries
Dittrich, B., & Ryan, J. P. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/6/065006 · Cited by 140 · see citing works
Self-citationImproved and perfect actions in discrete gravity
Bahr, B., & Dittrich, B. (2009) · Physical Review D · doi:10.1103/physrevd.80.124030 · Cited by 138 · see citing works
Self-citationDiffeomorphism Symmetry in Quantum Gravity Models
Dittrich, B. (2009) · Advanced Science Letters · doi:10.1166/asl.2009.1022 · Cited by 123 · see citing works
Self-citationThe Geometry of Dynamical Triangulations
(1997) · Lecture Notes in Physics Monographs · doi:10.1007/978-3-540-69427-4 · Cited by 113 · see citing works
Critical behavior of dynamically triangulated quantum gravity in four dimensions
Agishtein, M. E., & Migdal, A. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90106-l · Cited by 104 · see citing works
Pachner, U. (1987) · Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg · doi:10.1007/bf02941601 · Cited by 104 · see citing works
Coarse graining methods for spin net and spin foam models
Dittrich, B., Eckert, F. C., & Martín-Benito, M. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/3/035008 · Cited by 103 · see citing works
Self-citationSpin foam models for quantum gravity from lattice path integrals
Bonzom, V. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.064028 · Cited by 100 · see citing works
Classical 6j-symbols and the tetrahedronPreprint
Ggg, G. G. G., Tttt, T. T., & Roberts, J. (1999) · Cited by 100 · see citing works
(Broken) Gauge symmetries and constraints in Regge calculus
Bahr, B., & Dittrich, B. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/22/225011 · Cited by 94 · see citing works
Self-citationPerfect discretization of reparametrization invariant path integrals
Bähr, B., Dittrich, B., & Steinhaus, S. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.105026 · Cited by 93 · see citing works
Self-citationClassical 6j-symbols and the tetrahedron
Roberts, J. (1999) · Geometry & Topology · doi:10.2140/gt.1999.3.21 · Cited by 92 · see citing works
The semiclassical limit of causal dynamical triangulations
Jan Ambjørn, A., Görlich, A., Jurkiewicz, J., Loll, R., Gizbert-Studnicki, J., & Trześniewski, T. (2011) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2011.03.019 · Cited by 88 · see citing works
Evidence for Asymptotic Safety from Lattice Quantum Gravity
Laiho, J., & Coumbe, D. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.161301 · Cited by 88 · see citing works
Phase transition in dually weighted colored tensor models
Benedetti, D., & Gurău, R. (2011) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2011.10.015 · Cited by 84 · see citing works
(Broken) Gauge Symmetries and Constraints in Regge Calculus
Bahr, B., & Dittrich, B. (2009) · Max Planck Digital Library · Cited by 84 · see citing works
Self-citationRegge calculus from a new angle
Bähr, B., & Dittrich, B. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/3/033010 · Cited by 82 · see citing works
Self-citationSimplicity in simplicial phase space
Dittrich, B., & Ryan, J. P. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.064026 · Cited by 81 · see citing works
Self-citationPhases of simplical quantum gravity in four dimensions estimates for the critical exponents
Hamber, H. W. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90409-i · Cited by 77 · see citing works
The face amplitude of spinfoam quantum gravity
Eugenio Bianchi, A., Regoli, D., & Carlo Rovelli, C. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/18/185009 · Cited by 72 · see citing works
Linearized dynamics from the 4-simplex Regge action
Dittrich, B., Freidel, L., & Simone Speziale, D. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.104020 · Cited by 72 · see citing works
Self-citationFrom covariant to canonical formulations of discrete gravity
Dittrich, B., & Höhn, P. A. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/15/155001 · Cited by 71 · see citing works
Self-citationOn the measure in simplicial gravity
Hamber, H. W., & Williams, R. M. (1999) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.59.064014 · Cited by 70 · see citing works
Dittrich, B., & Höhn, P. A. (2012) · Classical and Quantum Gravity · doi:10.1088/0264-9381/29/11/115009 · Cited by 69 · see citing works
Self-citationBahr, 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
Breaking and Restoring of Diffeomorphism Symmetry in Discrete Gravity
Bähr, B., Dittrich, B., Kowalski-Glikman, J., Durka, R., & Szczachor, M. (2009) · AIP conference proceedings · doi:10.1063/1.3284371 · Cited by 60 · see citing works
Self-citationCoarse-graining free theories with gauge symmetries: the linearized case
Bahr, B., Dittrich, B., & He, S. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/4/045009 · Cited by 59 · see citing works
Self-citationSpin Foam Quantization and AnomaliesPreprint
Martin Bojowald, A., & Pérez, A. (2003) · Cited by 56 · see citing works
Recent progress in Regge calculus
Williams, R. M. (1997) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(97)00355-1 · Cited by 54 · see citing works
Twisted geometries: A geometric parametrisation of SU(2) phase space
Speziale, S., & Freidel, L. (2010) · HAL (Le Centre pour la Communication Scientifique Directe) · Cited by 49 · see citing works
From lattice BF gauge theory to area–angle Regge calculus
Bonzom, V. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/15/155020 · Cited by 47 · see citing works
Gauge invariance in simplicial gravity
Hamber, H. W., & Williams, R. M. (1997) · Nuclear Physics B · doi:10.1016/s0550-3213(97)87467-6 · Cited by 45 · see citing works
Simplicial quantum gravity in three dimensions: Analytical and numerical results
Hamber, H. W., & Williams, R. M. (1993) · Physical Review D · doi:10.1103/physrevd.47.510 · Cited by 45 · see citing works
In quantum gravity, summing is refining
Carlo Rovelli, C., & Smerlak, M. (2012) · Classical and Quantum Gravity · doi:10.1088/0264-9381/29/5/055004 · Cited by 45 · see citing works
PATH INTEGRALS AND THE INDEFINITENESS OF THE GRAVITATIONAL ACTION
Gibbons, G. W., Hawking, S. W., & Perry, M. J. (1993) · WORLD SCIENTIFIC eBooks · doi:10.1142/9789814539395_0004 · Cited by 45 · see citing works
Recurrence relations for spin foam vertices
Bonzom, V., Livine, E. R., & Simone Speziale, D. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/12/125002 · Cited by 44 · see citing works
Spin Foam Models with Finite Groups
Bähr, B., Dittrich, B., & Ryan, J. P. (2013) · Journal of Gravity · doi:10.1155/2013/549824 · Cited by 40 · see citing works
Self-citationSpikes in quantum Regge calculus
Jan Ambjørn, A., Nielsen, J. L., Rolf, J., & Savvidy, G. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/12/009 · Cited by 36 · see citing works
Spin foam quantization and anomalies
Bojowald, M., & Perez, A. (2010) · General Relativity and Gravitation · doi:10.1007/s10714-009-0892-9 · Cited by 35 · see citing works
Hidden quantum gravity in 3D Feynman diagrams
Baratin, A., & Freidel, L. (2007) · Classical and Quantum Gravity · doi:10.1088/0264-9381/24/8/006 · Cited by 33 · see citing works
Asymptotic analysis of the Ponzano–Regge model for handlebodies
Dowdall, R. J., Gomes, H., & Hellmann, F. (2010) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/43/11/115203 · Cited by 31 · see citing works
Spin foam models and the Wheeler-DeWitt equation for the quantum 4-simplex
Bonzom, V. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.024009 · Cited by 31 · see citing works
Discretizing parametrized systems: the magic of Ditt-invariancePreprint
Rovelli, C. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1107.2310 · Cited by 31 · see citing works
Hidden quantum gravity in 4D Feynman diagrams: emergence of spin foams
Baratin, A., & Freidel, L. (2007) · Classical and Quantum Gravity · doi:10.1088/0264-9381/24/8/007 · Cited by 28 · see citing works
Asymptotics of 4d spin foam models
Barrett, J. W., Dowdall, R. J., Fairbairn, W. J., Gomes, H., Hellmann, F., & Roberto Pereira, B. (2010) · General Relativity and Gravitation · doi:10.1007/s10714-010-0983-7 · Cited by 28 · see citing works
Asymptotics of 4d spin foam models
Barrett, J. W., Dowdall, R. J., Fairbairn, W. J., Gomesa, H., Hellmann, F., & Roberto Pereira, B. (2010) · Cited by 28 · see citing works
Diffeomorphism invariant measure for finite-dimensional geometries
Menotti, P., & Peirano, P. P. (1997) · Nuclear Physics B · doi:10.1016/s0550-3213(97)00017-5 · Cited by 26 · see citing works
Invariants of PL Manifolds from Metrized Simplicial Complexes. Three-Dimensional Case
Korepanov, I. G. (2001) · Journal of Nonlinear Mathematical Physics · doi:10.2991/jnmp.2001.8.2.3 · Cited by 26 · see citing works
Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
Baratin, A., & Freidel, L. (2006) · CERN Document Server (European Organization for Nuclear Research) · Cited by 26 · see citing works
On knottings in the physical Hilbert space of LQG as given by the EPRL model
Bähr, B. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/4/045002 · Cited by 25 · see citing works
Invariants of PL manifolds from metrized simplicial complexes. Three-dimensional case
Korepanov, I. G. (2008) · Cited by 23 · see citing works
Approximate diffeomorphism invariance in near-flat simplicial geometries
Morse, P. A. (1992) · Classical and Quantum Gravity · doi:10.1088/0264-9381/9/11/014 · Cited by 22 · see citing works
Euclidean 4-Simplices and Invariants of Four-Dimensional Manifolds: I. Moves 3→3
Korepanov, I. G. (2002) · Theoretical and Mathematical Physics · doi:10.1023/a:1015971322591 · Cited by 20 · see citing works
Discretisations, Constraints and Diffeomorphisms in Quantum Gravity
Bähr, B. (2012) · Symmetry Integrability and Geometry Methods and Applications · doi:10.3842/sigma.2012.002 · Cited by 20 · 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
Spherical Tetrahedra and Invariants of 3-manifoldsPreprint
Taylor, Y. U., & Woodward, C. T. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0406228 · Cited by 10 · see citing works
Oriti, D. (2005) · Brazilian Journal of Physics · doi:10.1590/s0103-97332005000300019 · Cited by 9 · see citing works
Multidimensional analogues of the geometrics⇌t duality
Korepanov, I. G. (2000) · Theoretical and Mathematical Physics · doi:10.1007/bf02551073 · Cited by 5 · see citing works
Многомерные аналоги геометрической $sleftrightarrow t$ дуальности
Korepanov, I. G., & Korepanov, I. G. (2000) · Теоретическая и математическая физика · doi:10.4213/tmf632 · Cited by 4 · see citing works
Flagged first, then by citations
1 of the 85 references couldn’t be matched to a known paper.
Cited by
Sorted by citations
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
Tensorial Methods and Renormalization in Group Field Theories
Carrozza, S. (2014) · Springer theses · doi:10.1007/978-3-319-05867-2 · Cited by 106 · see citing works
Decorated tensor network renormalization for lattice gauge theories and spin foam models
Dittrich, B., Mizera, S., & Steinhaus, S. (2016) · New Journal of Physics · doi:10.1088/1367-2630/18/5/053009 · Cited by 97 · see citing works
Self-citationFrom the discrete to the continuous: towards a cylindrically consistent dynamics
Dittrich, B. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/12/123004 · Cited by 94 · see citing works
Self-citationThe Continuum Limit of Loop Quantum Gravity: A Framework for Solving the Theory
Dittrich, B. (2017) · WORLD SCIENTIFIC eBooks · doi:10.1142/9789813220003_0006 · Cited by 91 · see citing works
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Dittrich, B., & Steinhaus, S. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/12/123041 · Cited by 77 · see citing works
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Bähr, B., Dittrich, B., Hellmann, F., & Kamiński, W. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.044048 · Cited by 76 · see citing works
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Asante, S. K., Dittrich, B., & Haggard, H. M. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.231301 · Cited by 72 · see citing works
Self-citationEffective spin foam models for Lorentzian quantum gravity
Asante, S. K., Dittrich, B., & Padua-Argüelles, J. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac1b44 · Cited by 69 · see citing works
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Delcamp, C., & Dittrich, B. (2017) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aa8f24 · Cited by 68 · see citing works
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Dittrich, B., Schnetter, E., Seth, C., & Steinhaus, S. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.124050 · Cited by 53 · see citing works
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Dittrich, B., & Kamiński, W. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1311.1798 · Cited by 17 · see citing works
Self-citationModified graviton dynamics from spin foams: the area Regge action
Dittrich, B. (2024) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-024-05432-4 · Cited by 15 · see citing works
Self-citationSpin Foams, Refinement Limit, and Renormalization
Asante, S. K., Dittrich, B., & Steinhaus, S. (2023) · Springer eBooks · doi:10.1007/978-981-19-3079-9_106-1 · 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-citationHolographic 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-citationCosmological Constant from Condensation of Defect Excitations
Dittrich, B. (2018) · Universe · doi:10.3390/universe4070081 · Cited by 11 · see citing works
Self-citationThe Barrett–Crane model: asymptotic measure factor
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Self-citationSpikes and spines in 4D Lorentzian simplicial quantum gravity
Borissova, J. N., Dittrich, B., Qu, D., & Schiffer, M. (2024) · Journal of High Energy Physics · doi:10.1007/jhep10(2024)150 · Cited by 9 · see citing works
Self-citationHolographic Formulation of 3D Metric Gravity with Finite Boundaries
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Self-citationCanonical linearized Regge calculus: Counting lattice gravitons with Pachner moves
Höhn, P. A. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.91.124034 · Cited by 9 · see citing works
Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
Steinhaus, S. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.92.064007 · Cited by 10 · see citing works
Self-citationPerfect discretizations as a gateway to one-loop partition functions for 4D gravity
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Self-citationTensorial methods and renormalization
Orsay, L. (2013) · Cited by 7 · see citing works
Lorentzian quantum gravity via Pachner moves: one-loop evaluation
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Self-citationSpikes and spines in 3D Lorentzian simplicial quantum gravity
Borissova, J. N., Dittrich, B., Qu, D., & Schiffer, M. (2025) · Classical and Quantum Gravity · doi:10.1088/1361-6382/adaf02 · Cited by 5 · see citing works
Self-citationDerivation of the deformed Heisenberg algebra from discrete spacetime
Shah, N. A., Ashraf, S. S. Z., Shaikh, A., Yamin, Y., Sahoo, P. K., Bhat, A., Lone, S. A., Faizal, M., & Ahsan, M. A. H. (2025) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/ada79d · Cited by 4 · see citing works
Holographic description of boundary gravitons in (3+1) dimensions
Asante, S. K., Dittrich, B., & Haggard, H. M. (2019) · Radboud Repository (Radboud University) · Cited by 3 · see citing works
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Goeller, C. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2005.09985 · Cited by 2 · see citing works
Two Paths to Group Field Theories
Carrozza, S. (2014) · Springer theses · doi:10.1007/978-3-319-05867-2_2 · Cited by 1 · see citing works
World quantum gravity: quantum test objects and Synge’s world function
Jia, D. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac25de · Cited by 1 · see citing works
Jercher, A. F., Simão, J. D., & Steinhaus, S. (2025) · Classical and Quantum Gravity · doi:10.1088/1361-6382/adc8f1 · Cited by 1 · see citing works
Self-citationPerfect discretization of path integrals
Steinhaus, S. (2012) · Journal of Physics Conference Series · doi:10.1088/1742-6596/360/1/012025
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Banburski, A. (2017) · UWSpace (University of Waterloo)
Amplitudes in the Spin Foam Approach to Quantum Gravity
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Lorentzian quantum gravity via Pachner moves: one-loop evaluationPreprint
Borissova, J. N., & Dittrich, B. (2023) · arXiv (Cornell University) · doi:10.48550/arxiv.2303.07367
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Asante, S. K., Dittrich, B., & Steinhaus, S. (2024) · Springer eBooks · doi:10.1007/978-981-99-7681-2_106
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Amith, T. M., & Castro, A. (2025) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ade110
- Authors
- Dittrich, B., & Steinhaus, S.
- Affiliations
- Max Planck Society (DE)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2012-02-14
- Volume
- 85
- Issue
- 4
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2145762037
- Cited by
- 66
- References
- 85
- Citations by year
- 2025: 4 · 2024: 5 · 2023: 5 · 2022: 2 · 2021: 5 · 2020: 4 · 2019: 4 · 2018: 5 · 2017: 6 · 2016: 3 · 2015: 3 · 2014: 8 · 2013: 9 · 2012: 3
- FWCI
- 5.57
- 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)
- Max Planck Digital Library (submittedVersion, other-oa)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- 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
- path integral measure, discrete quantum gravity, Regge calculus, Pachner moves, diffeomorphism symmetry, spin foam models, Ponzano-Regge model, three-dimensional gravity, semiclassical limit
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.
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