Lorentzian spin foam amplitudes: graphical calculus and asymptotics

Abstract

The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics of this amplitude are studied in the limit when the representation parameters are large, for various cases of boundary data. It is shown that for boundary data corresponding to a Lorentzian simplex, the asymptotic formula has two terms, with phase plus or minus the Lorentzian signature Regge action for the 4-simplex geometry, multiplied by an Immirzi parameter. Other cases of boundary data are also considered, including a surprising contribution from Euclidean signature metrics.

30 pages. v2: references now appear. v3: presentation greatly improved (particularly diagrammatic calculus). Definition of "Regge state" now the same as in previous work; signs change in final formula as a result. v4: two references added

References in corpus (16)

• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• The loop-quantum-gravity vertex-amplitude
• Flipped spinfoam vertex and loop gravity
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• LQG propagator from the new spin foams
• The Ponzano-Regge model
• The complete LQG propagator: II. Asymptotic behavior of the vertex
• Path integral representation of spin foam models of 4d gravity
• Quantum gravity asymptotics from the SU(2) 15j symbol
• Regularization and finiteness of the Lorentzian LQG vertices
• Spin foam model from canonical quantization
• Asymptotic analysis of the Ponzano-Regge model for handlebodies
• Coherent states, constraint classes, and area operators in the new spin-foam models

Cited by in corpus (180)

• The Spin Foam Approach to Quantum Gravity
• A Short Review of Loop Quantum Gravity
• Twisted geometries: A geometric parametrisation of SU(2) phase space
• Problem of Time in Quantum Gravity
• The complete 1/N expansion of colored tensor models in arbitrary dimension
• Polyhedra in loop quantum gravity
• Coarse graining methods for spin net and spin foam models
• 4-dimensional Spin-foam Model with Quantum Lorentz Group
• Quantum deformation of two four-dimensional spin foam models
• Loop quantum gravity: the first twenty five years
• Non-commutative flux representation for loop quantum gravity
• Lost in Translation: Topological Singularities in Group Field Theory
• Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity
• SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry
• Spin Foams and Canonical Quantization
• Effective Spin Foam Models for Four-Dimensional Quantum Gravity
• Effective Spin Foam Models for Lorentzian Quantum Gravity
• Lifting SU(2) Spin Networks to Projected Spin Networks
• Lorentzian spinfoam propagator
• Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude
• Investigation of the Spinfoam Path integral with Quantum Cuboid Intertwiners
• SU(2) graph invariants, Regge actions and polytopes
• Quantum gravity asymptotics from the SU(2) 15j symbol
• Holonomy spin foam models: Asymptotic geometry of the partition function
• Generalized Spinfoams
• A spin foam model for general Lorentzian 4-geometries
• Four-dimensional Quantum Gravity with a Cosmological Constant from Three-dimensional Holomorphic Blocks
• Spinfoam fermions
• The twistorial structure of loop-gravity transition amplitudes
• Imaginary action, spinfoam asymptotics and the 'transplanckian' regime of loop quantum gravity
• Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity
• Boosting Wigner's nj-symbols
• Observational Exclusion of a Consistent Quantum Cosmology Scenario
• Holomorphic Simplicity Constraints for 4d Spinfoam Models
• A proposed proper EPRL vertex amplitude
• A high-performance code for EPRL spin foam amplitudes
• Anomalous dimension in semiclassical gravity
• Holomorphic Lorentzian Simplicity Constraints
• Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
• Spinfoams in the holomorphic representation
• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
• Discrete Gravity Models and Loop Quantum Gravity: a Short Review
• Semiclassical Analysis of Spinfoam Model with a Small Barbero-Immirzi Parameter
• Critical Overview of Loops and Foams
• On Spinfoam Models in Large Spin Regime
• A spin-foam vertex amplitude with the correct semiclassical limit
• Asymptotics of lowest unitary SL(2,C) invariants on graphs
• Discrete gravity dynamics from effective spin foams
• Twistor Networks and Covariant Twisted Geometries
• Many-nodes/many-links spinfoam: the homogeneous and isotropic case
• Improved Effective Dynamics of Loop-Quantum-Gravity Black Hole and Nariai Limit
• Path Integral Representation of Lorentzian Spinfoam Model, Asymptotics, and Simplicial Geometries
• Regge gravity from spinfoams
• Asymptotic analysis of spin foam amplitude with timelike triangles
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity
• Numerical analysis of spin foam dynamics and the flatness problem
• Asymptotic analysis of the EPRL model with timelike tetrahedra
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS3 characters
• Einstein Equation from Covariant Loop Quantum Gravity in Semiclassical Continuum Limit
• Linking covariant and canonical LQG II: Spin foam projector
• Simple model for quantum general relativity from loop quantum gravity
• An elementary introduction to loop quantum gravity
• Discrete Symmetries in Covariant LQG
• Spin foams with timelike surfaces
• Towards a Cosmological subsector of Spin Foam Quantum Gravity
• Asymptotic analysis of the Ponzano-Regge model for handlebodies
• Classical Machian Resolution of the Spacetime Reconstruction Problem
• Spin foam models and the Wheeler-DeWitt equation for the quantum 4-simplex
• A Primer of Group Theory for Loop Quantum Gravity and Spin-foams
• Emergence of gravity from spinfoams
• Divergences and Orientation in Spinfoams
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• Euclidean three-point function in loop and perturbative gravity
• How-To compute EPRL spin foam amplitudes
• Asymptotics of 4d spin foam models
• From spin foams to area metric dynamics to gravitons
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• Covariant Loop Quantum Gravity, Low Energy Perturbation Theory, and Einstein Gravity with High Curvature UV Corrections
• Towards effective actions for the continuum limit of spin foams
• Emergence of Spacetime in a restricted Spin-foam model
• The Complete Barrett-Crane Model and its Causal Structure
• Four-dimensional Spinfoam Quantum Gravity with Cosmological Constant: Finiteness and Semiclassical Limit
• First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian
• EPRL/FK Asymptotics and the Flatness Problem
• Emergent 4-dimensional linearized gravity from spin foam model
• On the Expansions in Spin Foam Cosmology
• Numerical computations of next-to-leading order corrections in spinfoam large-$j$ asymptotics
• Sub-leading asymptotic behaviour of area correlations in the Barrett-Crane model
• A note on the secondary simplicity constraints in loop quantum gravity
• Quantum Mechanics on SO(3) via Non-commutative Dual Variables
• Infrared divergences in the EPRL-FK Spin Foam model
• Twisted geometries, twistors and conformal transformations
• Analytic Continuation of Spin foam Models
• Curvature in spinfoams
• Learning about Quantum Gravity with a Couple of Nodes
• 2-vertex Lorentzian Spin Foam Amplitudes for Dipole Transitions
• Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases
• Asymptotic analysis of spin-foams with time-like faces in a new parameterisation
• The Lorentzian proper vertex amplitude: Asymptotics
• How to detect an anti-spacetime
• Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
• Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double-${\Delta }_3$ complex
• Coherent states for FLRW space-times in loop quantum gravity
• On Spinfoams Near a Classical Curvature Singularity
• Squeezed vacua in loop quantum gravity
• Spin-foams as semi-classical vertices: gluing constraints and a hybrid algorithm
• Numerical analysis of the self-energy in covariant Loop Quantum Gravity
• Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)
• The Lorentzian proper vertex amplitude: Classical analysis and quantum derivation
• The Construction of Spin Foam Vertex Amplitudes
• All 3-edge-connected relativistic BC and EPRL spin-networks are integrable
• Hamiltonian spinfoam gravity
• Summing bulk quantum numbers with Monte Carlo in spin foam theories
• The Wald entropy formula and loop quantum gravity
• Spinfoams and high performance computing
• A note on entanglement entropy and quantum geometry
• General relativity as the equation of state of spin foam
• Asymptotics of $\mathrm{SL}(2,\mathbb{C})$ coherent invariant tensors
• Discrete Gravity on Random Tensor Network and Holographic Rényi Entropy
• Area Law from Loop Quantum Gravity
• On the structure of a background independent quantum theory: Hamilton function, transition amplitudes, classical limit and continuous limit
• Holonomy-flux spinfoam amplitude
• Radiative corrections to the Lorentzian EPRL spin foam propagator
• Lorentzian quantum cosmology from effective spin foams
• Canonical formulation of Poincare BFCG theory and its quantization
• One vertex spin-foams with the Dipole Cosmology boundary
• Parity and reality properties of the EPRL spinfoam
• Tullio Regge's legacy: Regge calculus and discrete gravity
• Spinfoams: Foundations
• Spin foam amplitude of the black-to-white hole transition
• The Barrett-Crane model: asymptotic measure factor
• Finiteness of spinfoam vertex amplitude with timelike polyhedra, and the full amplitude
• The thermodynamics of quantum spacetime histories
• Effective action for EPRL/FK spin foam models
• A finiteness bound for the EPRL/FK spin foam model
• The new spin foam models and quantum gravity
• Cosine problem in EPRL/FK spinfoam model
• A Short and Subjective Introduction to the Spinfoam Framework for Quantum Gravity
• Area Propagator and Boosted Spin Networks in Loop Quantum Gravity
• State Sums and Geometry
• Loop-Quantum-Gravity Simplicity Constraint as Surface Defect in Complex Chern-Simons Theory
• Poincare-Plebanski formulation of GR and dual simplicity constraints
• Classical dynamics for Loop Gravity: The 2-vertex model
• On the Asymptotics of Quantum Group Spinfoam Model
• Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data
• Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions
• Semiclassical Behavior of Spinfoam Amplitude with Small Spins and Entanglement Entropy
• A note on quantum supergravity and AdS/CFT
• Short-scale Emergence of Classical Geometry, in Euclidean Loop Quantum Gravity
• Curvature effects in the spectral dimension of spin foams
• Spinfoam cosmology with the proper vertex amplitude
• Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity
• Loop quantum gravity, twistors, and some perspectives on the problem of time
• Causal structure in spin-foams
• A Monte Carlo algorithm for spin foam intertwiners
• Geometry from local flatness in Lorentzian spin foam theories
• Spin foams
• Probing the Shape of Quantum Surfaces: the Quadrupole Moment Operator
• Hessian and graviton propagator of the proper vertex
• Spin foam propagator: A new perspective to include a cosmological constant
• Radiative corrections to the EPRL-FK spinfoam graviton
• The hessian in spin foam models
• A note on the spinor construction of Spin Foam amplitudes
• No invariant perfect qubit codes
• Deformations of Lorentzian Polyhedra: Kapovich-Millson phase space and SU(1,1) Intertwiners
• A look at area Regge calculus
• Cosmological states in loop quantum gravity on homogeneous graphs
• A Model of Spinfoam Coupled with an Environment
• Partial absence of cosine problem in 3d Lorentzian spin foams
• Studying the EPRL spinfoam self-energy
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Causal structure and topology change in (2+1)-dimensional simplicial gravity
• Spinfoam tunneling of quantum geometries in angle variables
• A saddle-point finder and its application to the spin foam model
• (2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality
• Boundary State Stability under Spinfoam Evolution for the Quantum 4-Simplex
• On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity
• Volume of 4-polytopes from bivectors
• Hessian in the spinfoam models with cosmological constant
• q-Deformation of Lorentzian spin foam models