Tullio Regge's legacy: Regge calculus and discrete gravity

Abstract

The review paper "Discrete Structures in Physics", written in 2000, describes how Regge's discretization of Einstein's theory has been applied in classical relativity and quantum gravity. Here, developments since 2000 are reviewed briefly, with particular emphasis on progress in quantum gravity through spin foam models and group field theories.

15 pages; a contribution to the forthcoming volume "Tullio Regge: an eclectic genius, from quantum gravity to computer play", Eds. L Castellani, A. Ceresole, R. D'Auria and P. Frè (World Scientific); v2: added references to more relevant work, minor changes to the text

References in corpus (16)

• LQG vertex with finite Immirzi parameter
• Group field theory with non-commutative metric variables
• Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude
• Cosmological perturbations from full quantum gravity
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS3 characters
• Gravitational Wilson Loop and Large Scale Curvature
• Dynamics of anisotropies close to a cosmological bounce in quantum gravity
• Constraints on Gravitational Scaling Dimensions from Non-Local Effective Field Equations
• A Discrete Representation of Einstein's Geometric Theory of Gravitation: The Fundamental Role of Dual Tessellations in Regge Calculus
• Canonical linearized Regge Calculus: counting lattice gravitons with Pachner moves
• Appearing Out of Nowhere: The Emergence of Spacetime in Quantum Gravity
• Disappearance and emergence of space and time in quantum gravity
• Aspects of Causality in the Parallelisable Implicit Evolution Scheme
• Regge calculus: a unique tool for numerical relativity
• (2+1) Regge Calculus: Discrete Curvatures, Bianchi Identity, and Gauss-Codazzi Equation

Cited by in corpus (8)

• Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects
• Time-space duality in 2D quantum gravity
• Analysis of curvature approximations via covariant curl and incompatibility for Regge metrics
• Oscillating 4-Polytopal Universe in Regge Calculus
• Light ray fluctuation and lattice refinement of simplicial quantum gravity
• Models of Discrete Linear Evolution for Quantum Systems
• Simplicial Gravity with Coordinates
• Discrete Black Holes