Quantum deformation of two four-dimensional spin foam models

Abstract

We construct the q-deformed version of two four-dimensional spin foam models, the Euclidean and Lorentzian versions of the EPRL model. The q-deformed models are based on the representation theory of two copies of U_q(su(2)) at a root of unity and on the quantum Lorentz group with a real deformation parameter. For both models we give a definition of the quantum EPRL intertwiners, study their convergence and braiding properties and construct an amplitude for the four-simplexes. We find that both of the resulting models are convergent.

45 pages, 4 figures, typos corrected, references added, proofs and explanations extended for readability

References in corpus (11)

• 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
• Quantum gravity with a positive cosmological constant
• 4-dimensional Spin-foam Model with Quantum Lorentz Group
• Face amplitude of spinfoam quantum gravity
• Path integral representation of spin foam models of 4d gravity
• Regularization and finiteness of the Lorentzian LQG vertices
• A new look at loop quantum gravity

Cited by in corpus (73)

• Loop Quantum Cosmology: A Status Report
• The Spin Foam Approach to Quantum Gravity
• A Short Review of Loop Quantum Gravity
• Decorated tensor network renormalization for lattice gauge theories and spin foam models
• Loop quantum gravity: the first twenty five years
• 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
• Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy
• Towards a phase diagram for spin foams
• Hypercuboidal renormalization in spin foam quantum gravity
• Cosmological constant in spinfoam cosmology
• Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory
• Coarse graining flow of spin foam intertwiners
• Four-dimensional Quantum Gravity with a Cosmological Constant from Three-dimensional Holomorphic Blocks
• Observables in Loop Quantum Gravity with a cosmological constant
• Coarse graining of spin net models: dynamics of intertwiners
• Quantum group spin nets: refinement limit and relation to spin foams
• Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
• Encoding Curved Tetrahedra in Face Holonomies: a Phase Space of Shapes from Group-Valued Moment Maps
• On Spinfoam Models in Large Spin Regime
• Semiclassical Analysis of Spinfoam Model with a Small Barbero-Immirzi Parameter
• Compact phase space, cosmological constant, discrete time
• Path Integral Representation of Lorentzian Spinfoam Model, Asymptotics, and Simplicial Geometries
• Poincare 2-group and quantum gravity
• Asymptotic analysis of the EPRL model with timelike tetrahedra
• Turaev-Viro amplitudes from 2+1 Loop Quantum Gravity
• Quantum hyperbolic geometry in loop quantum gravity with cosmological constant
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• Divergences and Orientation in Spinfoams
• Euclidean three-point function in loop and perturbative gravity
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• Emergence of Spacetime in a restricted Spin-foam model
• Covariant Loop Quantum Gravity, Low Energy Perturbation Theory, and Einstein Gravity with High Curvature UV Corrections
• A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity
• Four-dimensional Spinfoam Quantum Gravity with Cosmological Constant: Finiteness and Semiclassical Limit
• Spinors and Voros star-product for Group Field Theory: First Contact
• Emergent 4-dimensional linearized gravity from spin foam model
• Quantum deformation of quantum cosmology: A framework to discuss the cosmological constant problem
• Modified cosmology from quantum deformed entropy
• Typicality in spin network states of quantum geometry
• Anyonic statistics and large horizon diffeomorphisms for Loop Quantum Gravity Black Holes
• Topological lattice field theories from intertwiner dynamics
• The Construction of Spin Foam Vertex Amplitudes
• On the structure of a background independent quantum theory: Hamilton function, transition amplitudes, classical limit and continuous limit
• Our Universe from the cosmological constant
• On a self-dual phase space for 3+1 lattice Yang-Mills theory
• Lorentzian quantum cosmology from effective spin foams
• Symplectic and Semiclassical Aspects of the Schläfli Identity
• Deformation of the EPRL spin foam model by a cosmological constant
• The Poincaré group as a Drinfel'd double
• Spinfoams: Foundations
• SU(2) Flat Connection on Riemann Surface and Twisted Geometry with Cosmological Constant
• Finiteness of spinfoam vertex amplitude with timelike polyhedra, and the full amplitude
• Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
• The new spin foam models and quantum gravity
• On the Asymptotics of Quantum Group Spinfoam Model
• Loop-Quantum-Gravity Simplicity Constraint as Surface Defect in Complex Chern-Simons Theory
• Holographic relations in loop quantum gravity
• Canonical transformations generated by the boundary volume: Unimodular and non-Abelian teleparallel gravity
• A note on quantum supergravity and AdS/CFT
• Toward matter dynamics in spin foam quantum gravity
• Curvature effects in the spectral dimension of spin foams
• Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity
• Short-scale Emergence of Classical Geometry, in Euclidean Loop Quantum Gravity
• Recurrence relation for the 6j-symbol of su_q(2) as a symmetric eigenvalue problem
• On the dynamical emergence of $S{U}_q(2)$ from the regularization of $2+1D$ gravity with cosmological constant
• Quantum Groups and Polymer Quantum Mechanics
• Volume of 4-polytopes from bivectors
• q-Deformation of Lorentzian spin foam models
• Hessian in the spinfoam models with cosmological constant
• Remarks on SU_q(2) fermions
• Introduction to Spin Networks and Towards a Generalization of the Decomposition Theorem