Discretization independence implies non-locality in 4D discrete quantum gravity
arXiv:1404.5288 · doi:10.1088/0264-9381/31/24/245009
Abstract
The 4D Regge action is invariant under 5--1 and 4--2 Pachner moves, which define a subset of (local) changes of the triangulation. Given this fact one might hope to find a local path integral measure that makes the quantum theory invariant under these moves and hence makes the theory partially triangulation invariant. We show that such a local invariant path integral measure does not exist for the 4D linearized Regge theory. To this end we uncover an interesting geometric interpretation for the Hessian of the 4D Regge action. This geometric interpretation will allow us to prove that the determinant of the Hessian of the 4D Regge action does not factorize over 4--simplices or subsimplices. It furthermore allows to determine configurations where this Hessian vanishes, which only appears to be the case in degenerate backgrounds or if one allows for different orientations of the simplices. We suggest a non--local measure factor that absorbs the non--local part of the determinant of the Hessian under 5--1 moves as well as a local measure factor that is preserved for very special configurations.
18 pages, 6 figures; added references and clarifications
References in corpus (50)
- Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
- The Spin Foam Approach to Quantum Gravity
- Tensor renormalization group approach to 2D classical lattice models
- Perfect lattice action for asymptotically free theories
- Colored Tensor Models - a Review
- Prospects for perfect actions
- Diffeomorphisms and spin foam models
- Phase space descriptions for simplicial 4d geometries
- Improved and Perfect Actions in Discrete Gravity
- The Ponzano-Regge model
- Area-angle variables for general relativity
- From the discrete to the continuous - towards a cylindrically consistent dynamics
- Perfect discretization of reparametrization invariant path integrals
- Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity
- Regge calculus from a new angle
- Simplicity in simplicial phase space
- A note on area variables in Regge calculus
- Self-energy and vertex radiative corrections in LQG
- Linearized dynamics from the 4-simplex Regge action
- On the Measure in Simplicial Gravity
- Path integral measure and triangulation independence in discrete gravity
- Canonical simplicial gravity
- Breaking and restoring of diffeomorphism symmetry in discrete gravity
- Operator Spin Foam Models
- Coarse graining free theories with gauge symmetries: the linearized case
- Recent Progress in Regge Calculus
- First order Regge calculus
- Coarse graining of spin net models: dynamics of intertwiners
- Quantum group spin nets: refinement limit and relation to spin foams
- Gauge Invariance in Simplicial Gravity
- Constraint analysis for variational discrete systems
- On the role of the Barbero-Immirzi parameter in discrete quantum gravity
- Dirac's discrete hypersurface deformation algebras
- Bubble divergences and gauge symmetries in spin foams
- Spin Foam Quantization and Anomalies
- Hidden Quantum Gravity in 3d Feynman diagrams
- Divergences and Orientation in Spinfoams
- Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
- Constraints on Area Variables in Regge Calculus
- Invariants of PL manifolds from metrized simplicial complexes. Three-dimensional case
- Diffeomorphism invariant measure for finite dimensional geometries
- Pushing Further the Asymptotics of the 6j-symbol
- On knottings in the physical Hilbert space of LQG as given by the EPRL model
- Quantization of systems with temporally varying discretization II: Local evolution moves
- Quantization of systems with temporally varying discretization I: Evolving Hilbert spaces
- The 6j-symbol: Recursion, Correlations and Asymptotics
- The Ponzano-Regge asymptotic of the 6j symbol: an elementary proof
- The Barrett-Crane model: asymptotic measure factor
- Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions
- Multidimensional analogs of geometric s<-->t duality
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- Decorated tensor network renormalization for lattice gauge theories and spin foam models
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- Coarse graining flow of spin foam intertwiners
- Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
- Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
- Discrete gravity dynamics from effective spin foams
- Pachner moves in a 4d Riemannian holomorphic Spin Foam model
- Towards a Cosmological subsector of Spin Foam Quantum Gravity
- 3D holography: from discretum to continuum
- From spin foams to area metric dynamics to gravitons
- Lorentzian quantum cosmology goes simplicial
- (3+1)-dimensional topological phases and self-dual quantum geometries encoded on Heegard surfaces
- Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects
- Bulk amplitude and degree of divergence in 4d spin foams
- Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
- Holographic description of boundary gravitons in (3+1) dimensions
- De Sitter horizon entropy from a simplicial Lorentzian path integral
- Spikes and spines in 4D Lorentzian simplicial quantum gravity
- Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
- Perfect discretizations as a gateway to one-loop partition functions for 4D gravity
- A new realization of quantum geometry
- Modified Graviton Dynamics From Spin Foams: The Area Regge Action
- Quasi-Local 3D Quantum Gravity : Exact Amplitude and Holography
- (2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality
- Lorentzian quantum gravity via Pachner moves: one-loop evaluation
- Non-Ultralocality and Causality in the Relational Framework of Canonical Quantum Gravity