3+1 spinfoam model of quantum gravity with spacelike and timelike components

Abstract

We present a spinfoam formulation of Lorentzian quantum General Relativity. The theory is based on a simple generalization of an Euclidean model defined in terms of a field theory over a group. The model is an extension of a recently introduced Lorentzian model, in which both timelike and spacelike components are included. The spinfoams in the model, corresponding to quantized 4-geometries, carry a natural non-perturbative local causal structure induced by the geometry of the algebra of the internal gauge (sl(2,C)). Amplitudes can be expressed as integrals over the spacelike unit-vectors hyperboloid in Minkowski space, or the imaginary Lobachevskian space.

16 pages, 1 figure

References in corpus (7)

• Spacetime as a Feynman diagram: the connection formulation
• A spin foam model without bubble divergences
• Spin foam model for Lorentzian General Relativity
• Finiteness of a spinfoam model for euclidean quantum general relativity
• Gluing 4-simplices: a derivation of the Barrett-Crane spin foam model for Euclidean quantum gravity
• Integrability for Relativistic Spin Networks
• A lattice quantum gravity model with surface-like excitations in 4-dimensional spacetime

Cited by in corpus (42)

• Background Independent Quantum Gravity: A Status Report
• The Spin Foam Approach to Quantum Gravity
• LQG vertex with finite Immirzi parameter
• Spin Foam Models for Quantum Gravity
• A New Spin Foam Model for 4d Gravity
• Homogeneous cosmologies as group field theory condensates
• Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity
• Spin Foams and Canonical Quantization
• Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop Gravity
• Lorentzian LQG vertex amplitude
• Cosmological Deformation of Lorentzian Spin Foam Models
• Spin Networks for Non-Compact Groups
• A spin foam model for general Lorentzian 4-geometries
• Implementing causality in the spin foam quantum geometry
• Spinfoam fermions
• Barrett-Crane spin foam model from generalized BF-type action for gravity
• A finiteness proof for the Lorentzian state sum spinfoam model for quantum general relativity
• Hilbert space structure of covariant loop quantum gravity
• Critical Overview of Loops and Foams
• Asymptotic analysis of the EPRL model with timelike tetrahedra
• Timelike surfaces in Lorentz covariant loop gravity and spin foam models
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• The Complete Barrett-Crane Model and its Causal Structure
• Mean-field phase transitions in TGFT quantum gravity
• Boundary terms in the Barrett-Crane spin foam model and consistent gluing
• Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models
• Timelike twisted geometries
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
• The new spin foam models and quantum gravity
• Scalar Cosmological Perturbations from Quantum Gravitational Entanglement
• Finiteness and Dual Variables for Lorentzian Spin Foam Models
• Spin foam quantization of SO(4) Plebanski's action
• Rigorous construction of a Spin Foam Model for Lorentzian BF theory and Gravity: The foundations
• Reality Conditions for Spin Foams
• Relating Spin Foams and Canonical Quantum Gravity: A Discrete Step Evolution Formulation of Spin Foams
• Spin Foams for the Real, Complex Orthogonal Groups in 4D and the bivector scalar product reality constraint
• Scale invariance beyond criticality within the mean-field analysis of tensorial field theories
• Ashtekar Formulation with Temporal Foliations
• Spin Foam Models of Gravity and BF Theory as evolution of Spin Networks
• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model
• Spin Foams for the SO(4,C) BF theory and the SO(4,C) General Relativity