The DOI matches its Crossref record; 52 of the 73 references it cites were found in a registry or an index, and 21 are not checked yet; none of the 22 sources its claims cite is checked for support yet.
LQG vertex with finite Immirzi parameter
Open accessChecked 2026-10-06 · 21 references not checked yet
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper extends the flipped loop-quantum-gravity vertex to finite Immirzi parameter γ in both Euclidean and Lorentzian cases. It shows that the resulting boundary Hilbert space and area spectrum match loop quantum gravity, with the area spectrum discrete and γ-dependent, and the ad hoc symplectic flip no longer required.
Key findings
- A spinfoam model is defined for finite γ in both Euclidean and Lorentzian signatures; the boundary space is spanned by SU(2) spin networks, matching LQG on a fixed graph.
- The area operator has the same discrete spectrum as LQG, including the correct γ dependence, in both Euclidean and Lorentzian cases; imposing the simplicity constraints reduces the previously continuous covariant-LQG spectrum to the exact discrete LQG spectrum.
- In the Euclidean case, the diagonal constraint fixes the ratio of Spin(4) Casimirs; solutions select the highest SU(2) irreducible for γ < 1 and the lowest for γ > 1, with γ = 1 as the turning point, and impose a quantization condition on γ because the labels j± are half-integers.
- In the Lorentzian case, solutions are ρ = γn or ρ = −n/γ; the second constraint selects ρ = γn and k = n/2, the lowest SU(2) irreducible, so the continuous label ρ becomes effectively quantized because n is discrete. The ad hoc flip of the symplectic structure is not required for finite γ.
Methods
- The theory is discretized on a fixed Regge-like triangulation and dual 2-complex, with boundary variables B_f(t), holonomies U_f(t,t′), and conjugate J_f(t); constraints include closure, diagonal simplicity, and off-diagonal simplicity, with the latter reformulated using an internal normal vector n^I to select the B = ⋆e ∧ e sector.
- Quantization uses L²(G)^L with G = Spin(4) in the Euclidean case and G = SL(2,C) in the Lorentzian case; the diagonal constraint is imposed strongly, while the off-diagonal constraints are imposed via a master constraint, then projections to SU(2) spin networks and vertex amplitudes are derived.
- The area operators A and A₃ are analyzed using the constraints to obtain the spectrum.
Limitations
- The paper states that it leaves open whether the Lorentzian vertex is finite or needs regulation, whether spinfoam finiteness results extend to this model, the complete background-independent GFT construction, checking the graviton propagator, and understanding the results in terms of coherent states.
- The paper also notes an ordering ambiguity in the Casimir operators that may favor an area spectrum with regular spacing such as j or j + 1/2 instead of the standard √(j(j+1)), and that it is unclear whether a non-timelike choice for n^I is viable in the Lorentzian case.
- Evident from the supplied text: several displayed equations are omitted, so the algebraic derivations and exact formulas cannot be independently checked from this snapshot.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
0 of 22 cited sources checked · 0 supported · 0 flagged
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Group averaging over Spin (4) defines then the physical intertwiner space for the node e .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The off-diagonal simplicity constraints select the SU (2) irreducible with the spin determined by (27) in each of the two factors.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This construction defines also an embedding from the SU (2) spin networks to the Spin (4) spin networks on Γ.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The diagonal simplicity constraint restricts the direct sum to spins satisfying (25).”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Notice also that the continuous label ρ becomes quantized, because n is discrete.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The ad hoc flip of the symplectic structure that was required to derive the flipped vertex is not anymore required for finite γ .”
- Also stated in: § I. INTRODUCTION · p. 2 · plain
“is not required in the finite γ case.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
- Also stated in: § I. INTRODUCTION · p. 2 · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The constraint (17) fixes the ratio between these two Casimirs in term of the Immirzi parameter γ .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
None of the sources cited for this claim have been checked yet.
In the paper
“Following [2, 3, 7], the amplitude of a single vertex bounded by ten SU (2) spins j ab , a, b = 1 , ..., 5 and five SU (2) intertwiners i a is given by”
What the sources say
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Imposing C e = 0 strongly on the states in H 0 selects in each link the lowest (resp. highest) SU (2) irreducible.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“It further imposes that k = n/ 2, where k again labels the subspaces diagonalizing L 2 .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
- It may state two separate claims as one. 13
- The quote only partly states this claim. 1
- Probably not a substantial claim. 10
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“However, in our framework, the second constraint (22) breaks this symmetry and select the first branch ρ = γn .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“For finite, non-trivial Immirzi parameter, both sectors in fact yield GR, but the value of the Newton constant and Immirzi parameter are different in each sector.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The closure for the B f is equivalent to the closure for the J f which, as noted above, will be imposed automatically by the dynamics.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: Geometry is flat on each 4-simplex; curvature is concentrated on the bones and is coded in the holonomy around the link of each face.
- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This condition is stronger than (6) since it selects only the desired B = ⋆ e ∧ e sector.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: Geometry is flat on each 4-simplex; curvature is concentrated on the bones and is coded in the holonomy around the link of each face.
- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We show that the resulting dynamics is defined on a Hilbert space isomorphic to the one of loop quantum gravity”
- Also stated in: § I. INTRODUCTION · p. 1 · plain
“Second, for all values of γ the state space precisely matches the one of LQG (on a fixed graph).”
- Also stated in: § VI. CONCLUSION · p. 7 · plain
“In both cases, the boundary space turns out to be the same as in LQG, spanned by SU (2) spin networks.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one. The quote only partly states this claim.
- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
- Also stated in: § I. INTRODUCTION · p. 1 · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The constraints (14) on the other hand do not close as a Poisson algebra and their imposition in the quantum theory is more subtle.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: Geometry is flat on each 4-simplex; curvature is concentrated on the bones and is coded in the holonomy around the link of each face.
- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The constraint (12) commutes with the others and can be imposed directly as a strong operator equation.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: Geometry is flat on each 4-simplex; curvature is concentrated on the bones and is coded in the holonomy around the link of each face.
- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“and that the area operator has the same discrete spectrum as in loop quantum gravity. This includes the correct dependence on γ , and, remarkably, holds in the lorentzian case as well.”
- Also stated in: § I. INTRODUCTION · p. 1 · plain
“Third, the spectrum of the area operator turns out to be discrete, and to be the same as in LQG, including the correct dependence on the Immirzi parameter γ .”
- Also stated in: § VI. CONCLUSION · p. 7 · plain
“The spectrum of the area operator too is the same as in LQG, both for the euclidean and the lorentzian sectors.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
- Also stated in: § I. INTRODUCTION · p. 1 · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This construction defines the projection from the SL (2 , C ) boundary Hilbert space to the SU (2) space.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The solution is that the area spectrum is continuous in spinfoams at the kinematical level, but it turns out to become discrete after proper implementation of the (second class) constraints.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Finally, we would like to point out that the ordering of the Casimir operators for SU (2) and SL (2 , C ) required to have meaningful simplicity constraints do not use the usual ordering but seems to select an area spectrum with a regular spacing such as j (or j + 1 / 2) instead of the standard √ j ( j +1).”
Strength:hedged· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
- The authors state this as an assumption: The Immirzi parameter γ is finite and not 0 or 1.
In the paper
“A GFT yielding the new vertex amplitude is indeed already considered in [12].”
What the sources say
- Not checked yetcites [12]
Strength:boosted· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“The vertex was defined in [2, 3] only for the euclidean case, and in the absence of an Immirzi parameter γ .”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may state two separate claims as one.
In the paper
“Furthermore, the spectrum of the geometrical operators in this formulation turns out to be quite different from the standard one of loop quantum gravity [14].”
What the sources say
- Not checked yetcites [14] source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
In the paper
“It was shown in [16] that any spinfoam model [17], as the one we define here, admits a group field theory (GFT) [18] formulation, which is triangulation independent.”
What the sources say
- Not checked yetcites [16] source
Strength:boosted· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“The original model of [2, 3] and the variant pointed out in [11] appear as limiting γ → 0 and γ → ∞ cases, respectively.”
What the sources say
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“A key step to extend the definition of this new vertex was taken in [7], where a lorentzian version of the vertex amplitude is constructed, still without γ .”
What the sources say
- Not checked yetcites [7]
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“All these models ([2, 3, 11, 12],) are defined by the same vertex, namely the square of the SU (2) Wigner 15 j symbol; they differ for the class of boundary states considered and their measure in the spinfoam sum.”
What the sources say
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may state two separate claims as one.
In the paper
“This variant has been extensively explored in [12], and extended to the case of finite γ > 1.”
What the sources say
- Not checked yetcites [12]
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
None of the sources cited for this claim have been checked yet.
In the paper
“A different vertex has been recently introduced in [2, 3]; its amplitude essentially given by the square of an SU (2) Wigner 15 j symbol.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
In the paper
“In [11], it was shown that these constraints can equivalently be solved using a different technique, based on coherent states, yielding the same result.”
What the sources say
- Not checked yetcites [11] source
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The authors state this as an assumption.
Geometry is flat on each 4-simplex; curvature is concentrated on the bones and is coded in the holonomy around the link of each face.
“Geometry is assumed to be flat on each 4-simplex; curvature is concentrated on the 'bones' f , and is coded in the holonomy around the 'link' of each f .”
The authors state this as an assumption.
The Immirzi parameter γ is finite and not 0 or 1.
“(see [20] and [13]) where we have assumed γ fi nite and = 0 , 1.”
The authors state this as an assumption.
The internal vector n^I is fixed to δ^I_0, the general case is recovered by gauge invariance, and in the lorentzian case this restricts all tetrahedra to be spacelike.
“In order to proceed, let us fix n I = δ 0 I . The general case will be recovered by gauge invariance. In the lorentzian case this choice restricts all tetrahedra to be spacelike”
The authors state this as an assumption.
Constraint (3) is assumed to hold prior to varying the action.
“(3) is assumed to hold prior to varying the action.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“A modification of the Barrett-Crane model was recently introduced in [168, 169] and extended for arbitrary Immirzi parameter in [164].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [164]
In the citing paper
“where the unbalanced spins j + , j -are j ± ab = γ ± j ab , γ ± = 1 ± γ 2 . (31”
From LQG propagator from the new spin foams (2009) · cites this paper as [19]
In the citing paper
“We restrict attention to Euclidean signature and Immirzi parameter smaller than one: 0 < γ < 1.In this case the two models coincide.”
From LQG propagator from the new spin foams (2009) · cites this paper as [19]
In the citing paper
“That definition is merely equivalent to that of [10-12], however we spell it out in our notation for the clarity and the sake of precision.”
From Spin-foams for all loop quantum gravity (2010) · cites this paper as [10]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Lorentzian γ is said to be restricted despite a continuous representation label
MinorThe Lorentzian section says γ is restricted as in the Euclidean case. But it states that ρ is real and selects ρ = γn; for any real γ and positive integer n, that choice supplies an allowed real ρ, so the stated conditions impose no analogous quantization of γ.
“Notice that there is restriction on the value of γ as there was in the Euclidean case.”
“The unitary representations in the principal series are labelled by ( n, ρ ), where n is a positive integer and ρ real [22, 23].”
Citations
Cites
Generalized Coherent States and Their Applications
Perelomov, A. M. (1986) · Springer eBooks · doi:10.1007/978-3-642-61629-7 · Cited by 3,566
Kiefer, C. (2004) · Cited by 2,981
Background independent quantum gravity: a status report
Ashtekar, A., & Lewandowski, J. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/15/r01 · Cited by 1,951
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 · cited 2×
“Furthermore, the spectrum of the geometrical operators in this formulation turns out to be quite different from the standard one of loop quantum gravity [14].”
BackgroundQuantum 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
Loop space representation of quantum general relativity
Rovelli, C., & Smolin, L. (1990) · Nuclear Physics B · doi:10.1016/0550-3213(90)90019-a · Cited by 806
Introduction to Modern Canonical Quantum General RelativityPreprint
Thiemann, T. (2001) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0110034 · Cited by 685
Quantum theory of geometry II: Volume operators
Ashtekar, A., & Lewandowski, J. (1997) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1997.v1.n2.a8 · Cited by 580
Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
Holst, S. (1996) · Physical Review D · doi:10.1103/physrevd.53.5966 · Cited by 576
Spin foam models for quantum gravity
Perez, A. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/6/202 · Cited by 532
Flagged first, then by citations
Research works printed but not linked: 2
- Rovelli, 1995, Nucl. Phys. B, 456, 734
- DePietri, 2000, Barrett–Crane model from a Boulatov–Ooguri field theory over a homogeneous space, Nucl. Phys. B, 574, 785, 10.1016/s0550-3213(00)00005-5 · DOI · Paper page
Cited by
Sorted by citations
Items 301–400 of 580
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 23
Polytopes in all dimensional loop quantum gravity
Long, G., & Ma, Y. (2022) · The European Physical Journal C · doi:10.1140/epjc/s10052-022-09988-2 · Cited by 19
The Plebanski sectors of the EPRL vertex
Engle, J. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/22/225003 · Cited by 22
Self-citationEfficient Simulation of Loop Quantum Gravity: A Scalable Linear-Optical Approach
Cohen, L., Brady, A. J., Huang, Z., Liu, H., Qu, D., Dowling, J. P., & Han, M. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.020501 · Cited by 20
Group field theory and simplicial quantum gravity
Oriti, D. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/14/145017 · Cited by 38
Entropy in the classical and quantum polymer black hole models
Livine, E. R., & Terno, D. R. (2012) · Classical and Quantum Gravity · doi:10.1088/0264-9381/29/22/224012 · Cited by 18
Self-citationSqueezed vacua in loop quantum gravityPreprint
Eugenio Bianchi, A., Guglielmon, J., Hackl, L., & Yokomizo, N. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1605.05356 · Cited by 27
Physical boundary state for the quantum tetrahedronPreprint
Livine, E. R., & Simone Speziale, D. (2007) · HAL · Cited by 18
Self-citationBulk amplitude and degree of divergence in 4D spin foams
Chen, L.-Q. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.104025 · Cited by 20
Analytic continuation of spinfoam models
Han, M., & Liu, H. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.024012 · Cited by 19
Topological lattice field theories from intertwiner dynamicsPreprint
Dittrich, B., & Kamiński, W. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1311.1798 · Cited by 25
Towards computational insights into the large-scale structure of spin foamsPreprint
Dittrich, B., & Eckert, F. C. (2012) · Cited by 17
Spontaneously broken Lorentz symmetry for Hamiltonian gravity
Gielen, S., & Wise, D. K. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.104013 · Cited by 18
Coherent states for FLRW space-times in loop quantum gravity
Magliaro, E., Marcianò, A., & Perini, C. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.044029 · Cited by 18
Lorentzian proper vertex amplitude: Classical analysis and quantum derivation
Engle, J., & Zipfel, A. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.064024 · Cited by 23
Self-citationThe Construction of Spin Foam Vertex Amplitudes
Eugenio Bianchi, A. (2013) · Symmetry Integrability and Geometry Methods and Applications · doi:10.3842/sigma.2013.008 · Cited by 19
Spinfoams near a classical curvature singularity
Han, M., & Zhang, M. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.104075 · Cited by 20
Vergeles, S. N. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/abebb5 · Cited by 20
Corner Symmetry and Quantum Geometry
Freidel, L., Geiller, M., & Wieland, W. (2023) · Springer eBooks · doi:10.1007/978-981-19-3079-9_107-1 · Cited by 31
Markov chain Monte Carlo methods for graph refinement in spinfoam cosmology
Frisoni, P., Gozzini, F., & Vidotto, F. (2023) · Classical and Quantum Gravity · doi:10.1088/1361-6382/acc5d6 · Cited by 22
SPIN-CUBE MODELS OF QUANTUM GRAVITY
Miković, A. R. (2013) · Reviews in Mathematical Physics · doi:10.1142/s0129055x13430083 · Cited by 16
Han, M. (2010) · Max Planck Digital Library · Cited by 16
1 The Plebanski sectors of the EPRL vertexPreprint
Engle, J. (2013) · Cited by 20
Self-citationSpin-foams as semiclassical vertices: Gluing constraints and a hybrid algorithm
Asante, S. K., Simão, J. D., & Steinhaus, S. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.046002 · Cited by 20
Summing bulk quantum numbers with Monte Carlo in spin foam theories
Donà, P., & Frisoni, P. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.106008 · Cited by 15
Anisotropic spinfoam cosmology
Rennert, J., & Sloan, D. (2013) · Classical and Quantum Gravity · doi:10.1088/0264-9381/31/1/015017 · Cited by 19
Perelomov-type coherent states of SO ( D + 1 ) in all-dimensional loop quantum gravity
Long, G., & Bodendorfer, N. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.102.126004 · Cited by 16
Numerical analysis of the self-energy in covariant loop quantum gravity
Frisoni, P., Gozzini, F., & Vidotto, F. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.106018 · Cited by 16
Modified 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 29
Wieland, W. (2013) · Classical and Quantum Gravity · doi:10.1088/0264-9381/31/2/025002 · Cited by 17
Observables in 3d spinfoam quantum gravity with fermions
Dowdall, R. J., & Fairbairn, W. J. (2010) · General Relativity and Gravitation · doi:10.1007/s10714-010-1107-0 · Cited by 13
Thermally correlated states in loop quantum gravity
Chirco, G., Carlo Rovelli, C., & Ruggiero, P. (2015) · Classical and Quantum Gravity · doi:10.1088/0264-9381/32/3/035011 · Cited by 15
On the relation between rigging inner product and master constraint direct integral decomposition
Han, M., & Thiemann, T. (2010) · Journal of Mathematical Physics · doi:10.1063/1.3486359 · Cited by 16
From coarse-graining to holography in loop quantum gravity
Livine, E. R. (2018) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/123/10001 · Cited by 20
Self-citationAsymptotics of loop quantum gravity fusion coefficients
Alesci, E., Bianchi, E., Magliaro, E., & Perini, C. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/9/095016 · Cited by 15
On-shell actions with lightlike boundary dataPreprint
Neiman, Y. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1212.2922 · Cited by 28
Volume simplicity constraint in the Engle-Livine-Pereira-Rovelli spin foam model
Bähr, B., & Belov, V. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.086009 · Cited by 14
Spinfoams and High-Performance Computing
Donà, P., Han, M., & Liu, H. (2023) · Springer eBooks · doi:10.1007/978-981-19-3079-9_100-1 · Cited by 14
Holomorphic Simplicity Constraints for 4d Riemannian Spinfoam Models
Dupuis, M., & Livine, E. R. (2012) · Journal of Physics Conference Series · doi:10.1088/1742-6596/360/1/012046 · Cited by 14
Self-citationThe closure constraint for the hyperbolic tetrahedron as a Bianchi identity
Charles, C., & Livine, E. R. (2017) · General Relativity and Gravitation · doi:10.1007/s10714-017-2255-2 · Cited by 15
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 36
Towards 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
Canonical formulation of Poincaré BFCG theory and its quantization
Miković, A. R., & Oliveira, M. A. (2015) · General Relativity and Gravitation · doi:10.1007/s10714-015-1900-x · Cited by 14
Spin-foam model for gravity coupled to massless scalar field
Kisielowski, M., & Lewandowski, J. (2019) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aafcc0 · Cited by 17
All 3-edge-connected relativistic BC and EPRL spin-networks are integrablePreprint
Kamiński, W. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1010.5384 · Cited by 14
Spin Foam Models with Finite GroupsPreprint
Bähr, B., Dittrich, B., & Ryan, J. P. (2011) · arXiv (Cornell University) · doi:10.17863/cam.13547 · Cited by 14
0 A Path Integral for the Master Constraint of Loop Quantum GravityPreprint
Han, M. (2010) · Cited by 16
Thermally correlated states in Loop Quantum Gravity
RUGGIERO, P. (2014) · Electronic Theses and Dissertations Repository (University of Pisa) · Cited by 14
Lorentzian Quantum Cosmology from Effective Spin Foams
Dittrich, B., & Padua-Argüelles, J. (2024) · Universe · doi:10.3390/universe10070296 · Cited by 15
Area law from loop quantum gravity
Hamma, A., Hung, L.-Y., Marcianò, A., & Zhang, M. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.064040 · Cited by 14
Second-order amplitudes in loop quantum gravity
Mamone, D., & Carlo Rovelli, C. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/24/245013 · Cited by 14
The kernel and the injectivity of the EPRL map
Kamiński, W., Kisielowski, M., & Lewandowski, J. (2012) · Classical and Quantum Gravity · doi:10.1088/0264-9381/29/8/085001 · Cited by 13
Magliaro, E., & Perini, C. (2012) · International Journal of Modern Physics D · doi:10.1142/s0218271812500903 · Cited by 12
Rennert, J. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.95.026002 · Cited by 16
Commuting Simplicity and Closure Constraints for 4D Spin Foam Models
Han, M., & Thiemann, T. (2013) · Max Planck Digital Library · Cited by 13
Asymptotics of $$\mathrm {SL}(2,{{\mathbb {C}}})$$ coherent invariant tensors
Donà, P., Fanizza, M., Martin-Dussaud, P., & Simone Speziale, D. (2021) · Communications in Mathematical Physics · doi:10.1007/s00220-021-04154-3 · Cited by 13
Canonical path integral measures for Holst and Plebanski gravity: I. Reduced phase space derivation
Engle, J., Han, M., & Thiemann, T. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/24/245014 · Cited by 23
Self-citationCarlo Rovelli, C. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1108.0832 · Cited by 19
Bodendorfer, N., & Zipfel, A. (2016) · Classical and Quantum Gravity · doi:10.1088/0264-9381/33/15/155014 · Cited by 15
Radiative corrections to the Lorentzian Engle-Pereira-Rovelli-Livine spin foam propagator
Donà, P., Frisoni, P., & Wilson-Ewing, E. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.066022 · Cited by 15
Experimental simulation of loop quantum gravity on a photonic chip
van der Meer, R., Huang, Z., Anguita, M. C., Qu, D., Hooijschuur, P., Liu, H., Han, M., Renema, J. J., & Cohen, L. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00702-y · Cited by 13
Ashtekar-Barbero holonomy on the hyperboloid: Immirzi parameter as a cutoff for quantum gravity
Charles, C., & Livine, E. R. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.92.124031 · Cited by 18
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 13
Hopf 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
Numerical evaluation of spin foam amplitudes beyond simplices
Allen, C., Girelli, F., & Steinhaus, S. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.066003 · Cited by 15
Spin foam amplitude of the black-to-white hole transition
Han, M., Qu, D., & Zhang, C. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.124055 · Cited by 13
Engle, J., & Simone Speziale, D. (2023) · Springer eBooks · doi:10.1007/978-981-19-3079-9_99-1 · Cited by 18
Self-citationOne vertex spin-foams with the dipole cosmology boundary
Kisielowski, M., Lewandowski, J., & Puchta, J. (2012) · Classical and Quantum Gravity · doi:10.1088/0264-9381/30/2/025007 · Cited by 12
Carlo Rovelli, C. (2012) · Lecture notes in physics · doi:10.1007/978-3-642-33036-0_3 · Cited by 10
A finiteness bound for the EPRL/FK spin foam model
Miković, A. R., & Vojinović, M. (2013) · Classical and Quantum Gravity · doi:10.1088/0264-9381/30/3/035001 · Cited by 12
Tullio Regge's legacy: Regge calculus and discrete gravityPreprint
Barrett, J. W., Oriti, D., & Williams, R. M. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1812.06193 · Cited by 11
Holonomy-flux spinfoam amplitudePreprint
Perini, C. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1211.4807 · Cited by 19
Twisted geometries are area-metric geometries
Dittrich, B., & Padua-Argüelles, J. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.026002 · Cited by 20
Parity and reality properties of the EPRL spinfoam
Neiman, Y. (2012) · Classical and Quantum Gravity · doi:10.1088/0264-9381/29/6/065008 · Cited by 10
The accidental flatness constraint does not mean a wrong classical limit
Engle, J., & Carlo Rovelli, C. (2022) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac655e · Cited by 10
Self-citationTimeless path integral for relativistic quantum mechanics
Chiou, D.-W. (2013) · Classical and Quantum Gravity · doi:10.1088/0264-9381/30/12/125004 · Cited by 10
Towards a Loop Quantum Gravity and Yang–Mills unification
Alexander, S., Marcianò, A., & Tacchi, R. A. (2012) · Physics Letters B · doi:10.1016/j.physletb.2012.07.034 · Cited by 14
The Barrett–Crane model: asymptotic measure factor
Kamiński, W., & Steinhaus, S. (2014) · Classical and Quantum Gravity · doi:10.1088/0264-9381/31/7/075014 · Cited by 10
Deformation of the Engle-Livine-Pereira-Rovelli spin foam model by a cosmological constant
Bähr, B., & Rabuffo, G. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.086010 · Cited by 11
TENSORIAL STRUCTURE OF THE LQG GRAVITON PROPAGATOR
Alesci, E. (2008) · International Journal of Modern Physics A · doi:10.1142/s0217751x0804007x · Cited by 13
Intertwiner dynamics in the flipped vertex
Alesci, E., Eugenio Bianchi, A., Magliaro, E., & Perini, C. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/18/185003 · Cited by 14
Effective action for EPRL/FK spin foam models
Miković, A. R., & Vojinović, M. (2012) · Journal of Physics Conference Series · doi:10.1088/1742-6596/360/1/012049 · Cited by 9
Thermodynamics of quantum spacetime histories
Smolin, L. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.104042 · Cited by 10
Area propagator and boosted spin networks in loop quantum gravity
Livine, E. R. (2019) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab32d4 · Cited by 9
Self-citationHan, M., Kamiński, W., & Liu, H. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.084034 · Cited by 9
Causal dynamical triangulations in the spincube model of quantum gravity
Vojinović, M. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.024058 · Cited by 9
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
Extracting Geometry from Quantum Spacetime
Bonder, Y., Chryssomalakos, C., & Sudarsky, D. (2018) · Foundations of Physics · doi:10.1007/s10701-018-0192-x · Cited by 9
The new spin foam models and quantum gravityPreprint
Pérez, A. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1205.0911 · Cited by 9
A note on black hole entropy in loop quantum gravity
Carlip, S. (2015) · Classical and Quantum Gravity · doi:10.1088/0264-9381/32/15/155009 · Cited by 20
Hamiltonian formulation of gravity as a spontaneously-broken gauge theory of the Lorentz group
Nikjoo, M., & Zlosnik, T. G. (2024) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ad1c84 · Cited by 8
Cosine problem in EPRL/FK spinfoam model
Vojinović, M. (2013) · General Relativity and Gravitation · doi:10.1007/s10714-013-1616-8 · Cited by 8
Decoherent Histories of Spin Networks
Schroeren, D. (2013) · Foundations of Physics · doi:10.1007/s10701-013-9698-4 · Cited by 8
Spinfoam cosmology with the proper vertex amplitude
Vilensky, I. (2017) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aa91f4 · Cited by 8
Topological invariant of 4-manifolds based on a 3-group
Radenković, T., & Vojinović, M. (2022) · Journal of High Energy Physics · doi:10.1007/jhep07(2022)105 · Cited by 8
Fractal Quantum Space-TimePreprint
Modesto, L. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0905.1665 · Cited by 8
Hellmann, F. (2011) · Nottingham ePrints (University of Nottingham) · doi:10.48550/arxiv.1102.1688 · Cited by 11
Spinfoam Models for Quantum Gravity
Livine, E. R. (2024) · Elsevier eBooks · doi:10.1016/b978-0-323-95703-8.00253-6 · Cited by 15
Self-citationTensorial methods and renormalization
Orsay, L. (2013) · Cited by 7
Causal Structure in Spin Foams
Eugenio Bianchi, A., & Martin-Dussaud, P. (2024) · Universe · doi:10.3390/universe10040181 · Cited by 13
Metadata
- Authors
- Engle, J., Livine, E., Pereira, R., & Rovelli, C.
- Affiliations
- Université de Toulon (FR)
- École Normale Supérieure de Lyon (FR)
- Corresponding author
- Livine, Etera
- Venue
- Nuclear Physics B
- Publisher
- Elsevier BV
- Published
- 2008-08
- Volume
- 799
- Issue
- 1-2
- Pages
- 136-149
- ISSN
- 0550-3213 (ISSN-L)
- OpenAlex
- W2043256764
- Cited by
- 584
- References
- 73
- Citations by year
- 2026: 11 · 2025: 18 · 2024: 23 · 2023: 25 · 2022: 17 · 2021: 27 · 2020: 18 · 2019: 23 · 2018: 24 · 2017: 24 · 2016: 39 · 2015: 20 · 2014: 41 · 2013: 66 · 2012: 55
- FWCI
- 38.65
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Nuclear Physics B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion)
- arXiv (Cornell University)
- Nuclear Physics B - Proceedings Supplements
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy 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, Immirzi parameter, symplectic structure, four-dimensional quantum gravity
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.
A language model drew the claims from the paper on 2026-10-06, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-06 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
