Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory

Abstract

We study the no gravity limit G_{N}-> 0 of the Ponzano-Regge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with Hadamard propagator) expressed as an abelian spin foam model. We show how the G_{N} expansion of the Ponzano-Regge amplitudes can be resummed. This leads to the conclusion that the dynamics of quantum particles coupled to quantum 3d gravity can be expressed in terms of an effective new non commutative field theory which respects the principles of doubly special relativity. We discuss the construction of Lorentzian spin foam models including Feynman propagators

46 pages, the wrong file was first submitted

References in corpus (6)

• Quantum gravity in terms of topological observables
• How far are we from the quantum theory of gravity?
• Ponzano-Regge model revisited II: Equivalence with Chern-Simons
• Observables in the Turaev-Viro and Crane-Yetter models
• Scalar field theory on $\kappa$-Minkowski space-time and Doubly Special Relativity
• The Feynman propagator for quantum gravity: spin foams, proper time, orientation, causality and timeless-ordering

Cited by in corpus (176)

• The Spin Foam Approach to Quantum Gravity
• The principle of relative locality
• Colored Tensor Models - a Review
• 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
• An Invitation to Higher Gauge Theory
• On the semiclassical limit of 4d spin foam models
• Group field theory with non-commutative metric variables
• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity
• Twisted Statistics in kappa-Minkowski Spacetime
• The Ponzano-Regge model
• Diffeomorphisms in group field theories
• Covariant realizations of kappa-deformed space
• U(N) Coherent States for Loop Quantum Gravity
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Ten questions on Group Field Theory (and their tentative answers)
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• Charged BTZ black holes in the context of massive gravity's rainbow
• Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model
• Non-commutative flux representation for loop quantum gravity
• Disordered locality in loop quantum gravity states
• Fusion basis for lattice gauge theory and loop quantum gravity
• From noncommutative kappa-Minkowski to Minkowski space-time
• Spin Foams and Canonical Quantization
• Quantum Gravity, Dynamical Phase Space and String Theory
• Group Integral Techniques for the Spinfoam Graviton Propagator
• 30 years in: Quo vadis generalized uncertainty principle?
• Solving 3d Gravity with Virasoro TQFT
• 3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
• 4d Deformed Special Relativity from Group Field Theories
• Path integral representation of spin foam models of 4d gravity
• Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
• Quantization maps, algebra representation and non-commutative Fourier transform for Lie groups
• Bounding bubbles: the vertex representation of 3d Group Field Theory and the suppression of pseudo-manifolds
• Holonomy spin foam models: Asymptotic geometry of the partition function
• Towards the graviton from spinfoams: higher order corrections in the 3d toy model
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Gravity induced from quantum spacetime
• Towards classical geometrodynamics from Group Field Theory hydrodynamics
• Symmetries of quantum space-time in 3 dimensions
• Holomorphic Simplicity Constraints for 4d Spinfoam Models
• Lorentz invariant field theory on kappa-Minkowski space
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
• Anomalous dimension in semiclassical gravity
• A Prehistory of n-Categorical Physics
• Living in Curved Momentum Space
• Group field theory formulation of 3d quantum gravity coupled to matter fields
• Infinite-Dimensional Representations of 2-Groups
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity
• A Deformed Poincare Invariance for Group Field Theories
• A Lagrangian approach to the Barrett-Crane spin foam model
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS3 characters
• Braided quantum field theories and their symmetries
• Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime
• Hidden Quantum Gravity in 3d Feynman diagrams
• Particles as Wilson lines of gravitational field
• Relational evolution of effectively interacting GFT quantum gravity condensates
• The Holst Spin Foam Model via Cubulations
• A model for the motion of a particle in a quantum background
• Gamma ray burst delay times probe the geometry of momentum space
• Fermions in three-dimensional spinfoam quantum gravity
• Gauge theories on quantum spaces
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
• Causality and matter propagation in 3d spin foam quantum gravity
• Doubly Special Relativity: facts and prospects
• Quantum gravity on a square graph
• Three Dimensional Loop Quantum Gravity: Particles and the Quantum Double
• The DSR-deformed relativistic symmetries and the relative locality of 3D quantum gravity
• Effective particle kinematics from Quantum Gravity
• Tensor model and dynamical generation of commutative nonassociative fuzzy spaces
• $\kappa$-deformed complex fields and discrete symmetries
• Spinors and Voros star-product for Group Field Theory: First Contact
• Generic predictions of quantum theories of gravity
• Extended matter coupled to BF theory
• (3+1)-dimensional topological phases and self-dual quantum geometries encoded on Heegard surfaces
• Doubly-Special Relativity: Facts, Myths and Some Key Open Issues
• Chern-Simons theory, Stokes' Theorem, and the Duflo map
• Kinematics of particles with quantum de Sitter symmetries
• Matrix Models as Non-commutative Field Theories on R^3
• Quantum Mechanics on SO(3) via Non-commutative Dual Variables
• Gauge Theories on Deformed Spaces
• Algebraic approach to quantum gravity II: noncommutative spacetime
• A Note on B-observables in Ponzano-Regge 3d Quantum Gravity
• Star product and interacting fields on $\kappa$-Minkowski space
• On Noncommutative Effects in Entropic Gravity
• Non-Perturbative 3D Quantum Gravity: Quantum Boundary States and Exact Partition Function
• Three dimensional Loop Quantum Gravity: towards a self-gravitating Quantum Field Theory
• Planck-scale-deformed relativistic symmetries and diffeomorphisms in momentum space
• The Relativistic Particle: Dirac observables and Feynman propagator
• Deformed Carroll particle from 2+1 gravity
• Kappa-deformation of phase space; generalized Poincare algebras and R-matrix
• Discrete and continuum third quantization of Gravity
• Coupling of spacetime atoms and spin foam renormalisation from group field theory
• Emergent non-commutative matter fields from Group Field Theory models of quantum spacetime
• Snyder Momentum Space in Relative Locality
• A 2-categorical state sum model
• 3d Quantum Gravity: Coarse-Graining and q-Deformation
• Projective Loop Quantum Gravity I. State Space
• The Construction of Spin Foam Vertex Amplitudes
• Observables in 3d spinfoam quantum gravity with fermions
• Encoding simplicial quantum geometry in group field theories
• Spinfoam Fermions: PCT Symmetry, Dirac Determinant, and Correlation Functions
• Quasitriangular structure and twisting of the 2+1 bicrossproduct model
• Towards a dual spin network basis for (3+1)d lattice gauge theories and topological phases
• Wilson loops, geometric operators and fermions in 3d group field theory
• On gravitational defects, particles and strings
• Quantum Gravity with Matter via Group Field Theory
• Beyond Fock space in three dimensional semiclassical gravity
• Physical boundary state for the quantum tetrahedron
• Coherent States for 3d Deformed Special Relativity: semi-classical points in a quantum flat spacetime
• Two-dimensional topological field theories coupled to four-dimensional BF theory
• Emergent matter from 3d generalised group field theories
• 6J Symbols Duality Relations
• N=2 supersymmetric spin foams in three dimensions
• Tensor models and 3-ary algebras
• Conserved Quantities in Background Independent Theories
• A bound on Planck-scale modifications of the energy-momentum composition rule from atomic interferometry
• BTZ Black Hole Entropy and the Turaev-Viro model
• The Cutkosky rule of three dimensional noncommutative field theory in Lie algebraic noncommutative spacetime
• Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
• Multi-particle systems in $\kappa$-Poincaré inspired by 2+1D gravity
• Digital finite quantum Riemannian geometries
• Weak associativity and deformation quantization
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Quantizations of D=3 Lorentz symmetry
• Noncommutative spaces and covariant formulation of statistical mechanics
• $q$-deformed 3D Loop Gravity on the Torus
• Scalar Field Theory in Curved Momentum Space
• The new spin foam models and quantum gravity
• Metastring Theory and Modular Space-time
• A Short and Subjective Introduction to the Spinfoam Framework for Quantum Gravity
• A New Recursion Relation for the 6j-Symbol
• $\kappa$--Rindler space
• A one-dimensional action for simplicial gravity in three dimensions
• Extended TQFT's and Quantum Gravity
• The Quantum Gravity Disk: Discrete Current Algebra
• Entropy bound for the photon gas in noncommutative spacetime
• Holonomy observables in Ponzano-Regge type state sum models
• On the space of generalized fluxes for loop quantum gravity
• Towards self dual Loop Quantum Gravity
• Spin foams
• Causal structure in spin-foams
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Canonical Analysis of Algebraic String Actions
• From simplicial Chern-Simons theory to the shadow invariant I
• From simplicial Chern-Simons theory to the shadow invariant II
• The particle interpretation of N = 1 supersymmetric spin foams
• A Field Theory Model With a New Lorentz-Invariant Energy Scale
• Tunneling of quantum geometries in spinfoams
• Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions
• Background independent duals of the harmonic oscillator
• One-loop unitarity of scalar field theories on Poincare invariant commutative nonassociative spacetimes
• Quantum Klein Space and Superspace
• Massive particles coupled with 2+1 dimensional gravity and noncommutative field theory
• Simplicial vs. Continuum String Theory and Loop Equations
• Partial absence of cosine problem in 3d Lorentzian spin foams
• Quasi-Local 3D Quantum Gravity : Exact Amplitude and Holography
• Noncommutative kappa-Minkowski phi4 theory: Construction, properties and propagation
• The Ponzano-Regge model and parametric representation
• Emergence of scalar matter from spinfoam model
• The Ponzano-Regge cylinder and Propagator for 3d quantum gravity
• Weighting bubbles in group field theory
• Spinfoam tunneling of quantum geometries in angle variables
• Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model
• 3D Quantum Gravity from Holomorphic Blocks
• (2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality
• World quantum gravity: Quantum test objects and Synge's world function
• Braided algebras and the kappa-deformed oscillators
• New insights in quantum geometry
• Abelian 2+1D Loop Quantum Gravity Coupled to a Scalar Field
• Motion in Quantum Gravity
• Three-dimensional gravity and deformations of relativistic symmetries
• 3-dimensional $\Lambda$-BMS Symmetry and its Deformations