Holonomy Spin Foam Models: Definition and Coarse Graining

Abstract

We propose a new holonomy formulation for spin foams, which naturally extends the theory space of lattice gauge theories. This allows current spin foam models to be defined on arbitrary two-complexes as well as to generalize current spin foam models to arbitrary, in particular finite groups. The similarity with standard lattice gauge theories allows to apply standard coarse graining methods, which for finite groups can now be easily considered numerically. We will summarize other holonomy and spin network formulations of spin foams and group field theories and explain how the different representations arise through variable transformations in the partition function. A companion paper will provide a description of boundary Hilbert spaces as well as a canonical dynamic encoded in transfer operators.

36 pages, 12 figures

References in corpus (39)

• Discreteness of area and volume in quantum gravity
• Quantum Theory of Gravity I: Area Operators
• The Spin Foam Approach to Quantum Gravity
• Tensor renormalization group approach to 2D classical lattice models
• LQG vertex with finite Immirzi parameter
• Relativistic spin networks and quantum gravity
• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
• Colored Group Field Theory
• On the semiclassical limit of 4d spin foam models
• Spacetime as a Feynman diagram: the connection formulation
• Improved and Perfect Actions in Discrete Gravity
• Spin-Foams for All Loop Quantum Gravity
• Area-angle variables for general relativity
• Coarse graining methods for spin net and spin foam models
• EPRL/FK Group Field Theory
• (Broken) Gauge Symmetries and Constraints in Regge Calculus
• From the discrete to the continuous - towards a cylindrically consistent dynamics
• Bubble divergences from cellular cohomology
• Perfect discretization of reparametrization invariant path integrals
• Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop Gravity
• Path integral measure and triangulation independence in discrete gravity
• Operator Spin Foam Models
• Coarse graining free theories with gauge symmetries: the linearized case
• From lattice BF gauge theory to area-angle Regge calculus
• Hilbert space structure of covariant loop quantum gravity
• Renormalization of Discrete Models without Background
• A Lagrangian approach to the Barrett-Crane spin foam model
• Spin Foam Quantization and Anomalies
• Asymptotics of 4d spin foam models
• On knottings in the physical Hilbert space of LQG as given by the EPRL model
• Dual variables and a connection picture for the Euclidean Barrett-Crane model
• Fractal Space-Time from Spin-Foams
• Operator Spin Foams: holonomy formulation and coarse graining
• Diffeomorphism symmetry in quantum gravity models
• Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
• Towards computational insights into the large-scale structure of spin foams
• Local spin foams

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• Numerical evidence for a phase transition in 4d spin foam quantum gravity
• From the discrete to the continuous - towards a cylindrically consistent dynamics
• Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks
• Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy
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• Hypercuboidal renormalization in spin foam quantum gravity
• Time evolution as refining, coarse graining and entangling
• Functional Renormalisation Group analysis of a Tensorial Group Field Theory on ${\mathbb{R}}^3$
• Investigation of the Spinfoam Path integral with Quantum Cuboid Intertwiners
• Coarse graining flow of spin foam intertwiners
• Renormalizable Group Field Theory beyond melonic diagrams: an example in rank four
• Coarse graining of spin net models: dynamics of intertwiners
• Generalized quantum gravity condensates for homogeneous geometries and cosmology
• Quantum group spin nets: refinement limit and relation to spin foams
• Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Pachner moves in a 4d Riemannian holomorphic Spin Foam model
• On the role of the Barbero-Immirzi parameter in discrete quantum gravity
• Einstein Equation from Covariant Loop Quantum Gravity in Semiclassical Continuum Limit
• Linking covariant and canonical LQG II: Spin foam projector
• Flux formulation of loop quantum gravity: Classical framework
• Bubble divergences and gauge symmetries in spin foams
• Towards a Cosmological subsector of Spin Foam Quantum Gravity
• Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
• Fisher Metric, Geometric Entanglement and Spin Networks
• Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
• From 3D topological quantum field theories to 4D models with defects
• Topological lattice field theories from intertwiner dynamics
• Holonomy-flux spinfoam amplitude
• Holographic description of boundary gravitons in (3+1) dimensions
• Hopf link volume simplicity constraints in spin foam models
• Deformation of the EPRL spin foam model by a cosmological constant
• The Barrett-Crane model: asymptotic measure factor
• Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
• Path integral renormalisation in loop quantum cosmology
• A new realization of quantum geometry
• Renormalisation with SU(1, 1) coherent states on the LQC Hilbert space
• Properties of the Hamiltonian Renormalisation and its application to quantum mechanics on the circle
• Semiclassical Behavior of Spinfoam Amplitude with Small Spins and Entanglement Entropy
• Entanglement entropy of physical states in hypercuboidally truncated spin foam quantum gravity
• Topological quantum field theory and quantum gravity
• Landau Theory of Causal Dynamical Triangulations