Group field theory formulation of 3d quantum gravity coupled to matter fields

Abstract

We present a new group field theory describing 3d Riemannian quantum gravity coupled to matter fields for any choice of spin and mass. The perturbative expansion of the partition function produces fat graphs colored with SU(2) algebraic data, from which one can reconstruct at once a 3-dimensional simplicial complex representing spacetime and its geometry, like in the Ponzano-Regge formulation of pure 3d quantum gravity, and the Feynman graphs for the matter fields. The model then assigns quantum amplitudes to these fat graphs given by spin foam models for gravity coupled to interacting massive spinning point particles, whose properties we discuss.

RevTeX; 28 pages, 21 figures

References in corpus (26)

• Spin Foam Models for Quantum Gravity
• QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories
• Partial observables
• A Model of Three-Dimensional Lattice Gravity
• Group Field Theory: An overview
• Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
• Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
• Introduction to Doubly Special Relativity
• Spacetime as a Feynman diagram: the connection formulation
• Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
• Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
• Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity
• Diffeomorphisms and spin foam models
• 2+1 gravity and Doubly Special Relativity
• Feynman Diagrams of Generalized Matrix Models and the Associated Manifolds in Dimension 4
• Fermions in Quantum Gravity
• Three dimensional loop quantum gravity: coupling to point particles
• A spin foam model for pure gauge theory coupled to quantum gravity
• Spin Foam Models of Matter Coupled to Gravity
• Quantization of Diffeomorphism-Invariant Theories with Fermions
• Introduction to Quantum-Gravity Phenomenology
• Feynman diagams coupled to three-dimensional quantum gravity
• Spin Foam Models of Yang-Mills Theory Coupled to Gravity
• Quantum Loop Representation for Fermions coupled to Einstein-Maxwell field
• Feynman loops and three-dimensional quantum gravity
• Strings as perturbations of evolving spin-networks

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• Lost in Translation: Topological Singularities in Group Field Theory
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• 4d Deformed Special Relativity from Group Field Theories
• Group field theory for quantum gravity minimally coupled to a scalar field
• Loop quantum cosmology from group field theory
• Laplacians on discrete and quantum geometries
• Causality and matter propagation in 3d spin foam quantum gravity
• Extended matter coupled to BF theory
• The Complete Barrett-Crane Model and its Causal Structure
• Gravitational Wilson Loop in Discrete Quantum Gravity
• A Note on B-observables in Ponzano-Regge 3d Quantum Gravity
• Two-point functions in (loop) quantum cosmology
• Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models
• Emergent gravitational dynamics from multi-BEC hydrodynamics?
• Emergent non-commutative matter fields from Group Field Theory models of quantum spacetime
• Coupling of spacetime atoms and spin foam renormalisation from group field theory
• Observables in 3d spinfoam quantum gravity with fermions
• Spinfoam Fermions: PCT Symmetry, Dirac Determinant, and Correlation Functions
• Emergent matter from 3d generalised group field theories
• Fermions in Loop Quantum Gravity and Resolution of Doubling Problem
• The particle interpretation of N = 1 supersymmetric spin foams
• Operator Ordering Ambiguity and Third Quantization
• Emergence of scalar matter from spinfoam model
• From Dimensional Reduction of 4d Spin Foam Model to Adding Non-Gravitational Fields to 3d Spin Foam Model