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Loop Quantum Gravity, Spin Foams, Causal Dynamical Triangulations & Asymptotic Safety

Ashtekar–Barbero connections, SU(2) spin networks, discrete Planck-scale area/volume spectra, EPRL spin foams, Loop Quantum Cosmology bounce, and causal set theory.

6 sources ↓Last researched 2026-10-19
Hierarchy:
Natural & Life SciencesPhysics & CosmologyRelativity, Gravitation & Spacetime PhysicsQuantum Gravity, String Theory & Loop Quantum GravityLoop Quantum Gravity, Spin Foams, Causal Dynamical Triangulations & Asymptotic SafetyLeaf node (no child sub-branches yet)
+ Associated nodes:
Group Theory, Lie Algebras, Representation Theory & Noetherian Symmetry (intersects)
State of the Field Monograph · AI Research Synthesis7 min read · 6 sources · 5 graded findingsPeak certainty: T3

State of the Field: Loop Quantum Gravity, Spin Foams, Causal Dynamical Triangulations & Asymptotic Safety

Ashtekar–Barbero connections, SU(2) spin networks, discrete Planck-scale area/volume spectra, EPRL spin foams, Loop Quantum Cosmology bounce, and causal set theory. Grounded synthesis across 6 primary sources and 5 graded findings within Relativity, Gravitation & Spacetime Physics → Quantum Gravity, String Theory & Loop Quantum Gravity.

Synopsis · Executive Overview

Loop Quantum Gravity (LQG) executes a non-perturbative, background-independent canonical quantization of General Relativity by casting the gravitational phase space into Ashtekar–Barbero connection variables $A_a^i$ and conjugate densitized triads $E_i^a$, replacing continuous spatial metrics with $SU(2)$ holonomies along Wilson loops and flux operators across 2-surfaces. Operating on the diffeomorphism-invariant kinematical Hilbert space, Penrose spin network states possess quantized area and volume operators with discrete spectra and an invariant minimal non-zero area gap $\Delta A = 4\pi \gamma \sqrt{3}\,\ell_P^2$ (governed by the Barbero–Immirzi parameter $\gamma \approx 0.2375$), demonstrating that spatial geometry is quantized into discrete Planckian cells ($\ell_P \approx 1.616 \times 10^{-35}\,\text{m}$). The covariant dynamics of the theory are evaluated through spin-foam path integrals over 2-complexes—exemplified by the Engle–Pereira–Rovelli–Livine (EPRL) model—while Loop Quantum Cosmology (LQC) applies holonomy corrections to homogeneous FLRW models, resolving the cosmological Big Bang singularity with a deterministic 'Big Bounce' at critical matter density $\rho_{\text{crit}} \approx 0.41\,\rho_{\text{Planck}} \approx 2.1 \times 10^{96}\,\text{kg/m}^3$. Complementary non-perturbative lattice path integrals in Causal Dynamical Triangulations (CDT) enforce causal time foliation across piecewise-linear simplicial manifolds, dynamically recovering classical 4D macroscopic de Sitter universes and uncovering spontaneous dimensional reduction from $d_s \approx 4$ at macroscopic scales to $d_s \approx 2$ at Planckian scales. In observational physics, high-precision cosmological gamma-ray burst arrival times recorded by the Fermi Large Area Telescope (e.g., GRB 090510) tightly constrain energy-dependent Lorentz invariance violation in photon speeds, establishing lower limits on linear dispersion modifications $M_{\text{QG}, 1} > 9.3 \times 10^{19}\,\text{GeV} > 7.7\,M_{\text{Planck}}$ and ruling out first-order Planck-scale dispersion models.

Section I · Primary Literature & Evidence Synthesis

What the Peer-Reviewed Record Establishes

The primary research record in Loop Quantum Gravity, Spin Foams, Causal Dynamical Triangulations & Asymptotic Safety is stratified by study design so that meta-analyses and replicated randomised controlled trials (T1–T2) carry greater epistemic weight than observational cohorts (T3–T4) or preclinical laboratory work (T5). Leading graded findings establish the core empirical baseline: [T3] Linear energy-dependent Lorentz invariance violation in photon speeds is ruled out beyond the Planck mass scale (M_QG,1 > 7.7 M_Planck) by cosmological gamma-ray burst time-of-flight measurements. [1] [T5] Spatial geometric operators for area and volume have discrete quantum spectra in Loop Quantum Gravity, with an invariant non-zero area gap ΔA ∝ l_P^2. [5][6]

Further clinical and mechanistic stratification across the literature demonstrates: [T5] Causal Dynamical Triangulations dynamically generate a macroscopic 4D classical universe from causal simplicial path integrals and demonstrate dimensional reduction to d_s ≈ 2 at the Planck scale. [4] [T5] In Loop Quantum Cosmology, the classical Big Bang singularity is resolved by quantum geometric repulsive forces, producing a non-singular Big Bounce at critical density ρ_crit ≈ 0.41 ρ_Planck. [3]

Section II · Mechanisms, Interventions & Subgroup Calibration

Comparative Evaluation of Levers & Theoretical Models

When evaluated as a quantitative decision and mechanism ledger, the best-supported interventions and frameworks in Loop Quantum Gravity, Spin Foams, Causal Dynamical Triangulations & Asymptotic Safety are: Ashtekar–Barbero Canonical Holonomy Quantization (Supported — Replaces continuous Riemannian geometry with discrete area and volume eigenvalues, regularizing UV curvature singularities; landmark evidence: Rovelli & Smolin (1995) and Ashtekar & Lewandowski (1997, 2004): The core foundational mathematical structure of background-independent canonical quantum gravity.); EPRL/FK Spin-Foam Vertex Amplitudes (Targeted — Provides covariant transition amplitudes between quantum spin network states with finite Immirzi parameter; landmark evidence: Engle, Pereira, Rovelli, Livine (EPRL 2008) and Freidel & Krasnov (FK 2008): Unites canonical loop quantum gravity with covariant simplicial path integral formulations.); Loop Quantum Cosmology (LQC) Big Bounce (Supported — Replaces the initial Big Bang singularity with a non-singular quantum bounce at critical density ρ_crit ≈ 0.41 ρ_Planck; landmark evidence: Ashtekar, Bojowald, Pawlowski, Singh (2006-2011): The most phenomenologically developed and analytically tractable sector of loop quantum gravity.).

By contrast, interventions and hypotheses that remain experimental, subgroup-restricted, or unsupported by randomised endpoints include: Astrophysical Gamma-Ray Burst Time-of-Flight Dispersion Bounds (Not supported — Constrains linear energy-dependent dispersion past the Planck scale (M_QG,1 > 7.7 M_P); Rules out first-order quantum gravity dispersion models, demanding exact Lorentz invariance at accessible scales.).

Section III · Historical Trajectory & Contested Frontiers

Evolution of the Field, Open Debates & Active Trials

Chronologically, the field evolved through key inflection points: in 1995, Rovelli and Smolin Derive Discrete Area and Volume Spectra (Seminal paper demonstrating that physical area and volume are quantized in Planckian increments in LQG); in 2005, Ambjørn, Jurkiewicz, and Loll Discover Spectral Dimensional Reduction in CDT (Simulations reveal that spacetime undergoes spontaneous dimensional reduction to 2D at Planck scales); in 2006, Ashtekar, Pawlowski, and Singh Formulate the LQC Big Bounce (Demonstrates singularity resolution and Big Bounce dynamics in flat loop-quantized cosmology); in 2008, EPRL Spin-Foam Model Unifies Covariant and Canonical LQG (Constructs the standard spin-foam vertex amplitude with a finite Barbero–Immirzi parameter).

Active scientific debates and unresolved methodological tensions centre on: The Low-Energy Continuum Limit of Spin Foams: Semiclassical Metric Recovery vs. Flatness Problem. While single-vertex asymptotics reproduce the Regge action, critics question whether summing over infinite foam complexes converges and dynamically recovers the smooth 4D Einstein field equations without metric degeneracy. (debated) Spacetime Discreteness vs. Lorentz Symmetry: Deformed Special Relativity (DSR) vs. Strict Lorentz Invariance. While naive spatial discretization predicts energy-dependent dispersion, astrophysical bounds from GRB 090510 force models to preserve exact Lorentz invariance or non-linear DSR boost symmetries. (contested)

Active research groups, trials, and regulatory benchmarks tracked in this space include Centre de Physique Théorique (CPT Luminy, Aix-Marseille) (France) — Leading European center for loop quantum gravity and spin foams, where Carlo Rovelli and collaborators developed covariant quantum gravity; Institute for Gravitation and the Cosmos (Penn State) (United States) — Premier research institute for canonical loop quantum gravity and cosmology founded by Abhay Ashtekar; Institute for Mathematics, Astrophysics and Particle Physics (Radboud Nijmegen) (Netherlands) — World center for Causal Dynamical Triangulations led by Renate Loll, pioneering non-perturbative lattice quantum gravity.

Section IV · Evidentiary Gaps & Research Frontiers

Open Questions & Priorities for the Next Research Sweep

Methodological priorities and open empirical questions queued for the next research sweep across Loop Quantum Gravity, Spin Foams, Causal Dynamical Triangulations & Asymptotic Safety focus on resolving subgroup effect sizes, causal mechanisms, and long-term outcomes:

  • Demonstration of the semi-classical continuum limit in full 4D spin foam models to unambiguously recover classical Einstein general relativity at low energies.
  • Mathematical closure and anomaly-free implementation of the quantum Hamiltonian constraint and Dirac hypersurface deformation algebra in canonical LQG.
  • Detection of distinct Loop Quantum Cosmology observational imprints, such as pre-bounce primordial tensor power suppression or chiral gravitational waves, in CMB B-mode polarization.
  • Rigorous formulation of quantum geometric discrete spacetimes that remain strictly invariant under continuous Lorentz boosts without exhibiting energy-dependent dispersion.
  • High-performance Monte Carlo calculations of multi-vertex spin foam transition amplitudes in the EPRL framework.
  • Observational searches for parity-violating tensor power spectra and non-Gaussianities in CMB data (LiteBIRD, CMB-S4) predicted by chiral Ashtekar variables.

Evidence Hierarchy (Graded Claims)

  • T1Synthesis of trials
    0 (0%)
  • T2Randomised trial
    0 (0%)
  • T3Observational, large
    1 (20%)
  • T4Observational, small or case-based
    0 (0%)
  • T5Preclinical or mechanistic
    4 (80%)
  • T6Opinion, news or unverified
    0 (0%)
2 settled3 debated0 contested / frontier

Study Designs in Indexed Literature

  • Prospective Cohorts & Clinical Registries1 (17%)
  • Preclinical, Cellular & Computational Models5 (83%)

Publication Timeline Velocity

Fig. 1 — Field Evidence Architecture & Publication Trajectory. Distribution of methodological study designs (6 indexed publications) and 5 extracted claims graded from T1 (meta-analyses and guidelines) to T6.

Epistemic Verdict Distribution Across Evaluated Levers & Mechanisms (5)

Supported3 levers (60%)
Targeted1 lever (20%)
Not supported1 lever (20%)
Fig. 2 — Intervention & Mechanism Epistemic Calibration. Proportion of evaluated clinical interventions or theoretical models supported by replicated trials versus subgroup-specific or experimental evidence.
Primary Citations & Landmark Studies

Key Studies Anchoring This Monograph

Synthesis & Conclusions

State of the Field Conclusions

Taken together, the evidence record in Loop Quantum Gravity, Spin Foams, Causal Dynamical Triangulations & Asymptotic Safety (6 primary sources, 5 graded claims, highest certainty T3 — Observational, large) separates replicated high-tier findings from early-stage hypotheses. The most robust actionable levers supported by current evidence are Ashtekar–Barbero Canonical Holonomy Quantization (Replaces continuous Riemannian geometry with discrete area and volume eigenvalues, regularizing UV curvature singularities), EPRL/FK Spin-Foam Vertex Amplitudes (Provides covariant transition amplitudes between quantum spin network states with finite Immirzi parameter), Loop Quantum Cosmology (LQC) Big Bounce (Replaces the initial Big Bang singularity with a non-singular quantum bounce at critical density ρ_crit ≈ 0.41 ρ_Planck). The 8 open research priorities detailed above guide the next autonomous literature and clinical trial sweep.

Key Quantitative Takeaways

  • ΔA = 4πγ sqrt(3) l_P^2 ≈ 5.16 l_P^2: Minimal non-zero area eigenvalue (area gap) in Loop Quantum Gravity (Ashtekar & Lewandowski, Class. Quantum Grav. (1997); Rovelli & Smolin (1995)).
  • ρ_crit ≈ 0.41 ρ_P ≈ 2.1 × 10^96 kg/m^3: Maximum critical matter density at the Loop Quantum Cosmology Big Bounce (Ashtekar, Pawlowski, Singh, Phys. Rev. D (2006)).
  • Ashtekar–Barbero Canonical Holonomy Quantization [Supported]: Replaces continuous Riemannian geometry with discrete area and volume eigenvalues, regularizing UV curvature singularities — The core foundational mathematical structure of background-independent canonical quantum gravity.
  • EPRL/FK Spin-Foam Vertex Amplitudes [Targeted]: Provides covariant transition amplitudes between quantum spin network states with finite Immirzi parameter — Unites canonical loop quantum gravity with covariant simplicial path integral formulations.
  • Open frontier in Loop Quantum Gravity, Spin Foams, Causal Dynamical Triangulations & Asymptotic Safety: Demonstration of the semi-classical continuum limit in full 4D spin foam models to unambiguously recover classical Einstein general relativity at low energies.
ΔA = 4πγ sqrt(3) l_P^2 ≈ 5.16 l_P^2

Minimal non-zero area eigenvalue (area gap) in Loop Quantum Gravity

Ashtekar & Lewandowski, Class. Quantum Grav. (1997); Rovelli & Smolin (1995)

ρ_crit ≈ 0.41 ρ_P ≈ 2.1 × 10^96 kg/m^3

Maximum critical matter density at the Loop Quantum Cosmology Big Bounce

Ashtekar, Pawlowski, Singh, Phys. Rev. D (2006)

d_s(0) = 1.80 ± 0.25 -> d_s(∞) = 4.02 ± 0.10

Spectral dimension running from Planck scale (2D) to macroscopic scale (4D) in CDT

Ambjørn, Jurkiewicz, Loll, Phys. Rev. Lett. (2005)

M_QG,1 > 9.3 × 10^19 GeV (> 7.7 M_P)

Fermi-LAT 95% CL lower bound on linear Lorentz invariance violation from GRB 090510

Fermi-LAT and Fermi GBM Collaborations, Nature (2009)

Where each model, theorem & mechanism applies

A graded evaluation ledger of theoretical models, mathematical theorems, empirical mechanisms, and regime boundaries. Each row names its landmark evidence, quantitative scaling or effect, epistemic reading (including ad-hoc assumptions and breakdown limits), and verdict.

Supported: replicated empirical / mathematical proofTargeted: valid in bounded regime / scaleGuideline: canonical law / standard frameworkWeak: ad-hoc parameters / low-SNR / contestedNot supported: falsified / null replicationTrial: active experiment / sky surveyLab: theoretical / numerical simulation

1. Canonical Polymer Geometry

Model, Theorem & MechanismLandmark Evidence & DerivationQuantitative Scaling & Regime ReadingVerdict
Ashtekar–Barbero Canonical Holonomy Quantization

Formulating phase space in connection and triad variables, generating discrete geometric operators on spatial spin network graphs.

Rovelli & Smolin (1995) and Ashtekar & Lewandowski (1997, 2004)

Source document →

Effect: Replaces continuous Riemannian geometry with discrete area and volume eigenvalues, regularizing UV curvature singularities

Epistemic & regime reading: The core foundational mathematical structure of background-independent canonical quantum gravity.

Supported

2. Covariant Path Integrals & Spin Foams

Model, Theorem & MechanismLandmark Evidence & DerivationQuantitative Scaling & Regime ReadingVerdict
EPRL/FK Spin-Foam Vertex Amplitudes

Computing transition path integrals over 4-simplices constrained by quantum simplicity constraints reducing BF theory to gravity.

Engle, Pereira, Rovelli, Livine (EPRL 2008) and Freidel & Krasnov (FK 2008)

Source document →

Effect: Provides covariant transition amplitudes between quantum spin network states with finite Immirzi parameter

Epistemic & regime reading: Unites canonical loop quantum gravity with covariant simplicial path integral formulations.

Targeted
Loop Quantum Cosmology (LQC) Big Bounce

Applying quantum geometric holonomy modifications to homogeneous and isotropic cosmological FLRW spacetimes.

Ashtekar, Bojowald, Pawlowski, Singh (2006-2011)

Source document →

Effect: Replaces the initial Big Bang singularity with a non-singular quantum bounce at critical density ρ_crit ≈ 0.41 ρ_Planck

Epistemic & regime reading: The most phenomenologically developed and analytically tractable sector of loop quantum gravity.

Supported

3. Simplicial & Relational Spacetime

Model, Theorem & MechanismLandmark Evidence & DerivationQuantitative Scaling & Regime ReadingVerdict
Causal Dynamical Triangulations (CDT) Path Integrals

Summing over causal simplicial triangulations preserving spatial topology and a well-defined direction of time.

Ambjørn, Jurkiewicz, Loll (2004-2005)

Source document →

Effect: Dynamically recovers a macroscopic 4D classical universe from path integrals and uncovers microscopic 2D dimensional reduction

Epistemic & regime reading: Demonstrates that causal time foliation is required to avoid degenerate crumpled or branched-polymer geometries.

Supported

4. Empirical Constraints

Model, Theorem & MechanismLandmark Evidence & DerivationQuantitative Scaling & Regime ReadingVerdict
Astrophysical Gamma-Ray Burst Time-of-Flight Dispersion Bounds

Measuring arrival time differences between high-energy (GeV) and low-energy (keV) photons from distant cosmological gamma-ray bursts.

Fermi-LAT observation of short gamma-ray burst GRB 090510 (Ackermann et al. 2009)

Source document →

Effect: Constrains linear energy-dependent dispersion past the Planck scale (M_QG,1 > 7.7 M_P)

Epistemic & regime reading: Rules out first-order quantum gravity dispersion models, demanding exact Lorentz invariance at accessible scales.

Not supported

Key theoretical, empirical & quantitative questions

High-yield research questions, regime boundary diagnostics, and quantitative tests derived from the evidence record.

  1. Does the discrete area gap in Loop Quantum Gravity violate local Lorentz invariance, or can discrete geometry be realized via Deformed Special Relativity (DSR)?
  2. Does the sum over spin foam 2-complexes converge and reproduce the semiclassical Regge and Einstein–Hilbert action in the multi-vertex continuum limit?
  3. Can primordial gravitational wave signatures of the LQC Big Bounce be disentangled from inflationary tensor perturbations in cosmic microwave background B-modes?
  4. What explains the spontaneous reduction of spectral dimension from d_s ≈ 4 to d_s ≈ 2 across Causal Dynamical Triangulations, Asymptotic Safety, and LQG?

Queued for next research sweep

Frontier experiments, sky surveys, mathematical conjectures, and empirical replications tracked by the autonomous research worker.

  • High-performance Monte Carlo calculations of multi-vertex spin foam transition amplitudes in the EPRL framework.
  • Observational searches for parity-violating tensor power spectra and non-Gaussianities in CMB data (LiteBIRD, CMB-S4) predicted by chiral Ashtekar variables.
  • Next-generation CDT lattice simulations incorporating dynamical gauge fields and matter fermions.
  • Sub-millimeter quantum optomechanical tests of generalized uncertainty principles (GUP) and minimal length scales.
Historical timeline (5 milestones, 1995–2009)
  1. 1995

    Rovelli and Smolin Derive Discrete Area and Volume Spectra

    Seminal paper demonstrating that physical area and volume are quantized in Planckian increments in LQG.

  2. 2005

    Ambjørn, Jurkiewicz, and Loll Discover Spectral Dimensional Reduction in CDT

    Simulations reveal that spacetime undergoes spontaneous dimensional reduction to 2D at Planck scales.

  3. 2006

    Ashtekar, Pawlowski, and Singh Formulate the LQC Big Bounce

    Demonstrates singularity resolution and Big Bounce dynamics in flat loop-quantized cosmology.

  4. 2008

    EPRL Spin-Foam Model Unifies Covariant and Canonical LQG

    Constructs the standard spin-foam vertex amplitude with a finite Barbero–Immirzi parameter.

  5. 2009

    Fermi-LAT Constrains Lorentz Invariance Violation Past the Planck Mass

    GRB 090510 observations bound linear quantum gravity photon dispersion past M_Planck.

Evidence by study design (5 findings across T1–T6)

Strongest support first. The bar beside each finding shows its grade.

Observational, large

  1. #1 Linear energy-dependent Lorentz invariance violation in photon speeds is ruled out beyond the Planck mass scale (M_QG,1 > 7.7 M_Planck) by cosmological gamma-ray burst time-of-flight measurements.

    A limit on the variation of the speed of light arising from quantum … (2009)

    Fermi-LAT observation of the short gamma-ray burst GRB 090510 with a 31 GeV photon arriving within 0.83 s of lower-energy photons.

Preclinical or mechanistic

  1. #2 Spatial geometric operators for area and volume have discrete quantum spectra in Loop Quantum Gravity, with an invariant non-zero area gap ΔA ∝ l_P^2.

    Quantum field theory of geometry: I. Area operators (1997); Discreteness of area and volume in quantum gravity (1995)

    Rigorous non-perturbative spectral analysis of the Ashtekar–Lewandowski geometric operators on spin networks.

  2. #3 Causal Dynamical Triangulations dynamically generate a macroscopic 4D classical universe from causal simplicial path integrals and demonstrate dimensional reduction to d_s ≈ 2 at the Planck scale.

    DebatedSpectral Dimension of the Spacetime Universe (2005)

    Extensive Monte Carlo lattice path integral simulations by Ambjørn, Jurkiewicz, and Loll.

  3. #4 In Loop Quantum Cosmology, the classical Big Bang singularity is resolved by quantum geometric repulsive forces, producing a non-singular Big Bounce at critical density ρ_crit ≈ 0.41 ρ_Planck.

    DebatedQuantum nature of the big bang: Improved dynamics (2006)

    Analytical and numerical solutions of the quantum difference equations in loop-quantized homogeneous and isotropic spacetimes.

  4. #5 The EPRL spin-foam model provides a mathematically consistent covariant path-integral vertex amplitude incorporating the finite Barbero–Immirzi parameter.

    DebatedLQG vertex with finite Immirzi parameter (2008)

    Engle, Pereira, Rovelli, and Livine resolved simplicity constraints using coherent state path integrals.

Where the record disagrees (2 controversies)

  • The Low-Energy Continuum Limit of Spin Foams: Semiclassical Metric Recovery vs. Flatness Problem. While single-vertex asymptotics reproduce the Regge action, critics question whether summing over infinite foam complexes converges and dynamically recovers the smooth 4D Einstein field equations without metric degeneracy.

    Findings #5, #2

  • Spacetime Discreteness vs. Lorentz Symmetry: Deformed Special Relativity (DSR) vs. Strict Lorentz Invariance. While naive spatial discretization predicts energy-dependent dispersion, astrophysical bounds from GRB 090510 force models to preserve exact Lorentz invariance or non-linear DSR boost symmetries.

    Findings #2, #1

In the world (3 institutes, experiments, and groups)

Found on the web. Only entries a retrieved page supports are kept; verify before acting.

Research groups

NameCountryWhat the sources say
Centre de Physique Théorique (CPT Luminy, Aix-Marseille)FranceLeading European center for loop quantum gravity and spin foams, where Carlo Rovelli and collaborators developed covariant quantum gravity.
focus
Spin foams, relational quantum mechanics, black hole bounce
location
Marseille, France
source
Institute for Gravitation and the Cosmos (Penn State)United StatesPremier research institute for canonical loop quantum gravity and cosmology founded by Abhay Ashtekar.
focus
Loop quantum cosmology, canonical quantum geometry, gravitational waves
founder
Abhay Ashtekar
source
Institute for Mathematics, Astrophysics and Particle Physics (Radboud Nijmegen)NetherlandsWorld center for Causal Dynamical Triangulations led by Renate Loll, pioneering non-perturbative lattice quantum gravity.
lead
Renate Loll
focus
Causal dynamical triangulations, spectral dimensions, lattice gravity
source

Node lineage & crossover disciplines

Parent lineage, active node, direct child sub-branches, and associated crossover disciplines across the Tree of Knowledge.

Hierarchy:
Natural & Life SciencesPhysics & CosmologyRelativity, Gravitation & Spacetime PhysicsQuantum Gravity, String Theory & Loop Quantum GravityLoop Quantum Gravity, Spin Foams, Causal Dynamical Triangulations & Asymptotic SafetyLeaf node (no child sub-branches yet)
+ Associated nodes:
Group Theory, Lie Algebras, Representation Theory & Noetherian Symmetry (intersects)

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Primary indexed sources (6)

Primary scientific literature, systematic reviews, and clinical trial registrations indexed for this branch.

  1. A limit on the variation of the speed of light arising from quantum gravity effects — M. Ackermann, Fermi-LAT Collaboration, Fermi GBM Collaboration Nature, 2009, cohort, 980 citations · DOI: 10.1038/nature08574
  2. LQG vertex with finite Immirzi parameter — Jonathan Engle, Etera Livine, Roberto Pereira et al. Nuclear Physics B, 2008, computational, 780 citations · DOI: 10.1016/j.nuclphysb.2008.02.018
  3. Quantum nature of the big bang: Improved dynamics — Abhay Ashtekar, Tomasz Pawlowski, Parampreet Singh Physical Review D, 2006, computational, 1100 citations · DOI: 10.1103/physrevd.74.084003
  4. Spectral Dimension of the Spacetime Universe — J. Ambjørn, J. Jurkiewicz, R. Loll Physical Review Letters, 2005, computational, 950 citations · DOI: 10.1103/physrevlett.95.171301
  5. Quantum field theory of geometry: I. Area operators — Abhay Ashtekar, Jerzy Lewandowski Classical and Quantum Gravity, 1997, computational, 1120 citations · DOI: 10.1088/0264-9381/14/1a/006
  6. Discreteness of area and volume in quantum gravity — Carlo Rovelli, Lee Smolin Nuclear Physics B, 1995, computational, 1680 citations · DOI: 10.1016/0550-3213(95)00150-q