A Lorentzian Signature Model for Quantum General Relativity

John W. Barrett; Louis Crane

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A Lorentzian Signature Model for Quantum General Relativity

John W. Barrett, Louis Crane

General Relativity and Quantum Cosmology · Submitted 9 Apr 1999

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The authors' main claim We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra.

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What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.62 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.91 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral given by an integral over suitable representations of this algebra. This generalises the state sum models for the case of the four-dimensional rotation group previously studied in gr-qc/9709028. As a technical tool, formulae for the evaluation of relativistic spin networks for the Lorentz group are developed, with some simple examples which show that the evaluation is finite in interesting cases. We conjecture that the `10J' symbol needed in our model has a finite value.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra.	contribution 0.94	0.91	0.17	asserted 1.00
s1	We propose a combinatorial model for the path integral given by an integral over suitable representations of this algebra.	contribution 0.52	0.80	0.14	asserted 0.77
s2	This generalises the state sum models for the case of the four-dimensional rotation group previously studied in gr-qc/9709028.	background 0.73	0.19	0.06	asserted 1.00
s3	As a technical tool, formulae for the evaluation of relativistic spin networks for the Lorentz group are developed, with some simple examples which show that the evaluation is finite in interesting cases.	contribution 0.49	0.93	0.07	asserted 1.00
s4	We conjecture that the `10J' symbol needed in our model has a finite value.	future work 0.42	0.20	0.19	speculative 1.00

What kind of paper the classifier reports this is: theoretical result 0.94 · evidence from proof or derivation 0.96.

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The paper

Original abstract

We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral given by an integral over suitable representations of this algebra. This generalises the state sum models for the case of the four-dimensional rotation group previously studied in gr-qc/9709028. As a technical tool, formulae for the evaluation of relativistic spin networks for the Lorentz group are developed, with some simple examples which show that the evaluation is finite in interesting cases. We conjecture that the `10J' symbol needed in our model has a finite value.

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References

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Cited by 21 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Constraining quantum-gravity predictions for evolving dark energy
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Edge modes of gravity. Part III. Corner simplicity constraints
hep-th 2020-07 conditional novelty 7.0 of 10

The corner area element equals the Poincaré spin Casimir, and the continuum simplicity constraints split into two second class and one first class component, leaving the full Lorentz algebra as Dirac observables.
A New Spin Foam Model for 4d Gravity
gr-qc 2007-08 conditional novelty 7.0 of 10

A new spin foam vertex is constructed that solders neighbouring tetrahedra, is argued to quantize the gravitational rather than the topological sector of Plebanski gravity, and admits a quantized Immirzi parameter.
Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
hep-th 2005-02 conditional novelty 7.0 of 10

The Ponzano-Regge spin foam amplitude with particle insertions reduces, as the Newton constant goes to zero, to ordinary Feynman diagram evaluation, and its full gravitational expansion resums into a braided non-commu...
Deep learning spinfoam vertex amplitudes: the Euclidean Barrett-Crane model
gr-qc 2025-05 conditional novelty 6.0 of 10

A proof-of-principle that simple neural networks can learn Euclidean Barrett-Crane 10j vertex amplitudes: classification generalizes to higher cutoffs, regression works only within the trained low-spin domain.

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A state sum for four-dimensional Lorentzian quantum geometry in terms of edge vectors
gr-qc 2025-01 conditional novelty 6.0 of 10

A new state sum model for 4D Lorentzian quantum gravity is constructed from quantum edge vectors and related to the Barrett-Crane spin foam model.
Spinfoams, $\gamma$-duality and parity violation in primordial gravitational waves
gr-qc 2024-03 unverdicted novelty 6.0 of 10

γ-duality in the EPRL spinfoam model determines the relation between parity-even and parity-odd terms in an effective gravity theory, allowing the Barbero-Immirzi parameter to be measured from inflationary tensor observables.
Tensorial methods and renormalization in Group Field Theories
hep-th 2013-10 conditional novelty 6.0 of 10

Group Field Theories with tensorial interactions and a closure constraint admit a consistent multiscale renormalization analysis, and a 3d SU(2) model is shown just-renormalizable at the perturbative level.
Lorentzian spin foam amplitudes: graphical calculus and asymptotics
gr-qc 2009-07 conditional novelty 6.0 of 10

In the large-spin limit the Lorentzian EPRL four-simplex amplitude oscillates with phase equal to plus or minus the Immirzi-scaled Lorentzian Regge action, and the proportionality of the two representation labels is f...
Quantum Gravity from Gluing Consistency: AdS/CFT to Spin-Foams
hep-th 2026-10 conditional novelty 5.0 of 10

This paper argues, with several internal consistency checks, that BF theory with conformal gauge group provides a universal gluing skeleton whose presentation-independence condition could bootstrap quantum gravity, li...
Causal structure in spin-foams
gr-qc 2021-09 unverdicted novelty 5.0 of 10

Proposes a causal EPRL spin-foam model where the two-complex orientation encodes causality and aids semiclassical geometry reconstruction.
Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model
gr-qc 2011-08 conditional novelty 5.0 of 10

Adding a dynamical normal vector to each tetrahedron in group field theory lets the simplicity constraints be imposed covariantly, yielding a Barrett-Crane-type spin foam model whose edge amplitudes differ from earlie...
Holomorphic Simplicity Constraints for 4d Spinfoam Models
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A holomorphic splitting of the simplicity constraints yields coherent intertwiners that solve them exactly, and a new spinfoam model is built from those states.
Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
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Weakening the simplicity constraints to hold only in expectation values, using coherent states, reproduces the Engle-Pereira-Rovelli spinfoam model and gives its boundary states a clear quantum-tetrahedron geometry.
Group Field Theory: An overview
hep-th 2005-05 conditional novelty 4.0 of 10

Group field theory's tree-level two-point function is proposed as a triangulation-independent physical inner product for loop quantum gravity, with the full two-point function giving a sum over spacetime topologies.
Group field theories
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Group field theory is presented as the generating functional for spin foam amplitudes, with a new explicit construction for the Lorentzian EPRL/FK model in four dimensions.
The group field theory approach to quantum gravity
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Group field theory recasts quantum gravity as an ordinary quantum field theory whose Feynman diagrams are discrete spacetimes, making spatial topology dynamical rather than fixed.
Les Houches lectures on Spinfoam Path Integrals
gr-qc 2026-07 accept novelty 2.0 of 10

A pedagogical review of spinfoam path integrals, from 1d quantum mechanics and 2d BF theory through Ponzano-Regge/Turaev-Viro to the 4d EPRL model, accurate but with no new results.
Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
hep-ph 2021-11 accept novelty 2.0 of 10

The review argues that multi-messenger astronomy now supplies workable empirical constraints on Planck-scale quantum gravity, chiefly through energy-dependent propagation effects accumulated over cosmological distances.
Zakopane lectures on loop gravity
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Introduction to Modern Canonical Quantum General Relativity
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How later papers used it

68 later papers cite it

Evidence: substantial. 68 of the citing papers share no author with it, and 6 of those carry a confident label from Pith's citation classifier.

Pith read 13 of the 132 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 compared its own results with it.

Compares with it 1 of 3 papers with this label

Said its new Lorentzian model has similar advantages as compared to this paper.

A New Spin Foam Model for 4d Gravity (2007) · 0.88 · paraphrased: the licence does not allow quoting

How the literature uses it

68 arXiv papers cite this in 133 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 74 sentences without a confident label

Contests it 1 paper

Unlike the rest of the constraints, the center is imposed strongly in the literature.[We also remind the reader that in the previous Barrett-Crane model [ref] , all constraints were imposed strongly, leading to inconsistencies.] This somewhat uneven procedure for the implementation is a motivation for our present work, where we consider the possibility of treating all constraints on the same footing.

Holomorphic Lorentzian Simplicity Constraints · Introduction · contest 0.84

Builds on it 1 paper

We constructed the complete BC model by extending existing formulations of the BC model: One which includes timelike normal vectors only [ref] and the other one which exclusively considers spacelike normal vectors [ref] .

The Complete Barrett-Crane Model and its Causal Structure · Relation to other GFT and spin foam models · 1.00

Uses its method or tool 2 papers

For a spin-network with the invariants from the set described above we can define the evaluation by the method proposed in [ref] . * Firstly, we consider the graph with links labelled by the representations of the principal series $(k_e,ρ_e)$ and nodes labelled by elements of $F$ in the tensor product of the representations associated with the links meeting in the node (as described in the case of compact groups).

All 3-edge-connected relativistic BC and EPRL spin-networks are integrable · The evaluation of the spin-network · 1.00
This is achieved as follows: * We utilize the rich causal structure of the completion [ref] of the Barrett-Crane (BC) GFT model [ref] , which provides a GFT quantization of first-order Palatini gravity, to causally couple a physical Lorentzian reference frame to the GFT model. * We represent slightly inhomogeneous cosmological geometries via entangled states $|Δ;x^0,*x⟩$.

Scalar Cosmological Perturbations from Quantum Gravitational Entanglement · Introduction · 0.91

Compares with it 3 papers

agreeing with the results obtained in [ref] .

The Complete Barrett-Crane Model and its Causal Structure · Kernels of non-mixed type · 0.99
The new Lorentzian model that we obtain has similar advantages as compared to [ref] .

A New Spin Foam Model for 4d Gravity · Introduction · 0.88
The complicate expressions of the above boost matrix elements can be compared with the much simpler ones appearing in the Lorentzian Barrett-Crane model [ref] .

Boosting Wigner's nj-symbols · Boost matrix elements for simple representations · 1.00

Cites it as background 44 papers

A main outcome in this longstanding direction of research during the previous decade has been what has become known as the EPRL spinfoam transition amplitude of (covariant) Loop Quantum Gravity [ref] .

Geometry Transition in Spinfoams · Introduction · 0.88
The two most developed and most studied models are the Barrett-Crane model (BC) [ref] and the Engle-Pereira-Rovelli-Livine (EPRL) model [ref] .

Spinfoam Models for Quantum Gravity: Overview · 4d Quantum Gravity · 0.93
The Barrett-Crane (BC) model [ref] and the EPRL model [ref] are the most prominent GFT (and spin foam) models, realizing a constrained BF-quantization of first-order Palatini and first-order Palatini-Holst gravity, respectively.

The Complete Barrett-Crane Model and its Causal Structure · Introduction · 0.92

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