Group field theory and simplicial quantum gravity

Abstract

We present a new Group Field Theory for 4d quantum gravity. It incorporates the constraints that give gravity from BF theory, and has quantum amplitudes with the explicit form of simplicial path integrals for 1st order gravity. The geometric interpretation of the variables and of the contributions to the quantum amplitudes is manifest. This allows a direct link with other simplicial gravity approaches, like quantum Regge calculus, in the form of the amplitudes of the model, and dynamical triangulations, which we show to correspond to a simple restriction of the same.

14 pages, no figures; RevTex4; v2: definition of the model modified, discussion extended and improved

References in corpus (25)

• LQG vertex with finite Immirzi parameter
• Spin Foam Models for Quantum Gravity
• Reconstructing the Universe
• A New Spin Foam Model for 4d Gravity
• The loop-quantum-gravity vertex-amplitude
• Group Field Theory: An overview
• Flipped spinfoam vertex and loop gravity
• Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
• The Universe from Scratch
• Group field theory renormalization - the 3d case: power counting of divergences
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• Hamiltonian Analysis of Plebanski Theory
• Noncommutative Harmonic Analysis, Sampling Theory and the Duflo Map in 2+1 Quantum Gravity
• Path integral representation of spin foam models of 4d gravity
• Implementing causality in the spin foam quantum geometry
• Simplicity and closure constraints in spin foam models of gravity
• From lattice BF gauge theory to area-angle Regge calculus
• Barrett-Crane spin foam model from generalized BF-type action for gravity
• The Feynman propagator for spin foam quantum gravity
• Plebanski Theory and Covariant Canonical Formulation
• Causality and matter propagation in 3d spin foam quantum gravity
• A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
• Generalised group field theories and quantum gravity transition amplitudes
• 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

Cited by in corpus (14)

• Tensor models and embedded Riemann surfaces
• Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
• Non-commutative flux representation for loop quantum gravity
• Radiative corrections in the Boulatov-Ooguri tensor model: The 2-point function
• Critical Overview of Loops and Foams
• Bubbles and jackets: new scaling bounds in topological group field theories
• Nonperturbative renormalization group beyond melonic sector: The Effective Vertex Expansion method for group fields theories
• Spin foam models and the Wheeler-DeWitt equation for the quantum 4-simplex
• Ward-constrained melonic renormalization group flow for the rank-four ${\varphi }^6$ tensorial group field theory
• Reliability of the local truncations for the random tensor models renormalization group flow
• Flowing in discrete gravity models and Ward identities: A review
• Corner symmetry and quantum geometry
• No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint
• Large-$d$ behavior of the Feynman amplitudes for a just-renormalizable tensorial group field theory