New action for simplicial gravity in four dimensions

Abstract

We develop a proposal for a theory of simplicial gravity with spinors as the fundamental configuration variables. The underlying action describes a mechanical system with finitely many degrees of freedom, the system has a Hamiltonian and local gauge symmetries. We will close with some comments on the resulting quantum theory, and explain the relation to loop quantum gravity and twisted geometries. The paper appears in parallel with an article by Cortês and Smolin, who study the relevance of the model for energetic causal sets and various other approaches to quantum gravity.

26 pages, 2 figures

References in corpus (40)

• Discreteness of area and volume in quantum gravity
• Real Ashtekar Variables for Lorentzian Signature Space-times
• LQG vertex with finite Immirzi parameter
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• Real and complex connections for canonical gravity
• The principle of relative locality
• ``Sum over Surfaces'' form of Loop Quantum Gravity
• Twisted geometries: A geometric parametrisation of SU(2) phase space
• Flipped spinfoam vertex and loop gravity
• Polyhedra in loop quantum gravity
• Metric-affine approach to teleparallel gravity
• Diffeomorphisms and spin foam models
• Phase space descriptions for simplicial 4d geometries
• SU(2) Loop Quantum Gravity seen from Covariant Theory
• From twistors to twisted geometries
• Why Gauge?
• Area-angle variables for general relativity
• Quantum tetrahedra and simplicial spin networks
• On the geometry of loop quantum gravity on a graph
• Regge calculus from a new angle
• Simplicity in simplicial phase space
• A note on area variables in Regge calculus
• The Universe as a Process of Unique Events
• Lifting SU(2) Spin Networks to Projected Spin Networks
• Discreteness of the volume of space from Bohr-Sommerfeld quantization
• Energetic Causal Sets
• Plebanski Formulation of General Relativity: A Practical Introduction
• First order Regge calculus
• The twistorial structure of loop-gravity transition amplitudes
• Holomorphic Lorentzian Simplicity Constraints
• Constraint analysis for variational discrete systems
• Gravity as BF theory plus potential
• The spin connection of twisted geometry
• Null twisted geometries
• Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases
• Hamiltonian spinfoam gravity
• A one-dimensional action for simplicial gravity in three dimensions
• ON NON-RIEMANNIAN PARALLEL TRANSPORT IN REGGE CALCULUS
• Area Regge calculus and continuum limit
• Regge Calculus in Teleparallel Gravity

Cited by in corpus (16)

• Edge modes of gravity -- I: Corner potentials and charges
• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Edge modes of gravity. Part III. Corner simplicity constraints
• New boundary variables for classical and quantum gravity on a null surface
• Boosting Wigner's nj-symbols
• A note on the secondary simplicity constraints in loop quantum gravity
• Twisted geometries, twistors and conformal transformations
• Spin foam models as energetic causal sets
• The dynamics of difference
• Realism and Causality II: Retrocausality in Energetic Causal Sets
• Corner symmetry and quantum geometry
• Hopf link volume simplicity constraints in spin foam models
• The thermodynamics of quantum spacetime histories
• A new realization of quantum geometry
• Quantum edge modes in 3d gravity and 2+1d topological phases of matter
• Causal structure in spin-foams