Regge calculus from a new angle
arXiv:0907.4325 · doi:10.1088/1367-2630/12/3/033010
Abstract
In Regge calculus space time is usually approximated by a triangulation with flat simplices. We present a formulation using simplices with constant sectional curvature adjusted to the presence of a cosmological constant. As we will show such a formulation allows to replace the length variables by 3d or 4d dihedral angles as basic variables. Moreover we will introduce a first order formulation, which in contrast to using flat simplices, does not require any constraints. These considerations could be useful for the construction of quantum gravity models with a cosmological constant.
8 pages
References in corpus (11)
- A New Spin Foam Model for 4d Gravity
- The loop-quantum-gravity vertex-amplitude
- Improved and Perfect Actions in Discrete Gravity
- Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
- Area-angle variables for general relativity
- (Broken) Gauge Symmetries and Constraints in Regge Calculus
- Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions
- Hidden Quantum Gravity in 3d Feynman diagrams
- Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
- 6j symbols for U_q(sl_2) and non-Euclidean tetrahedra
- Continuity of the Volume of Simplices in Classical Geometry
Cited by in corpus (65)
- Improved and Perfect Actions in Discrete Gravity
- 4-dimensional Spin-foam Model with Quantum Lorentz Group
- From the discrete to the continuous - towards a cylindrically consistent dynamics
- Perfect discretization of reparametrization invariant path integrals
- Fusion basis for lattice gauge theory and loop quantum gravity
- SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry
- Simplicity in simplicial phase space
- Effective Spin Foam Models for Four-Dimensional Quantum Gravity
- Effective Spin Foam Models for Lorentzian Quantum Gravity
- From covariant to canonical formulations of discrete gravity
- Path integral measure and triangulation independence in discrete gravity
- Canonical simplicial gravity
- Time evolution as refining, coarse graining and entangling
- Breaking and restoring of diffeomorphism symmetry in discrete gravity
- Coarse graining free theories with gauge symmetries: the linearized case
- On the regularization of the constraints algebra of Quantum Gravity in 2+1 dimensions with non-vanishing cosmological constant
- Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
- Quantum gravity kinematics from extended TQFTs
- Discrete gravity dynamics from effective spin foams
- Compact phase space, cosmological constant, discrete time
- Discretization independence implies non-locality in 4D discrete quantum gravity
- Towards the Turaev-Viro amplitudes from a Hamiltonian constraint
- Dirac's discrete hypersurface deformation algebras
- A Discrete and Coherent Basis of Intertwiners
- Towards a Cosmological subsector of Spin Foam Quantum Gravity
- 3D holography: from discretum to continuum
- Lorentzian quantum cosmology goes simplicial
- 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
- Spinfoam Cosmology: quantum cosmology from the full theory
- (3+1)-dimensional topological phases and self-dual quantum geometries encoded on Heegard surfaces
- Discretisations, Constraints and Diffeomorphisms in Quantum Gravity
- New action for simplicial gravity in four dimensions
- Wheeler-DeWitt Equation in 3 + 1 Dimensions
- From 3D topological quantum field theories to 4D models with defects
- Topological lattice field theories from intertwiner dynamics
- The Construction of Spin Foam Vertex Amplitudes
- Discrete Gravity on Random Tensor Network and Holographic Rényi Entropy
- Lorentzian quantum cosmology from effective spin foams
- De Sitter horizon entropy from a simplicial Lorentzian path integral
- Holographic description of boundary gravitons in (3+1) dimensions
- Symplectic and Semiclassical Aspects of the Schläfli Identity
- Tullio Regge's legacy: Regge calculus and discrete gravity
- 2-Group Representations for Spin Foams
- Being, Becoming and the Undivided Universe: A Dialogue between Relational Blockworld and the Implicate Order Concerning the Unification of Relativity and Quantum Theory
- Canonical linearized Regge Calculus: counting lattice gravitons with Pachner moves
- The Barrett-Crane model: asymptotic measure factor
- SU(2) Flat Connection on Riemann Surface and Twisted Geometry with Cosmological Constant
- Spikes and spines in 4D Lorentzian simplicial quantum gravity
- A new realization of quantum geometry
- Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions
- Tunneling of quantum geometries in spinfoams
- Fat Triangulations and Differential Geometry
- Generating Functionals for Spin Foam Amplitudes
- Spin foam propagator: A new perspective to include a cosmological constant
- On the linearization of Regge calculus
- Spinfoam tunneling of quantum geometries in angle variables
- Quasi-Local 3D Quantum Gravity : Exact Amplitude and Holography
- Lorentzian quantum gravity via Pachner moves: one-loop evaluation
- On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity
- Entropy of quantum channel in the theory of quantum information
- Gauge Invariance from a Graphical Self-Consistency Criterion
- Curvatures and discrete Gauss-Codazzi equation in (2+1)-dimensional loop quantum gravity
- Physical States and Transition Amplitudes in Piecewise Flat Quantum Gravity
- The massive BMS character in 3D quantum gravity
- Volume and Boundary Face Area of a Regular Tetrahedron in a Constant Curvature Space