Classical and quantum general relativity: a new paradigm

Abstract

We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory has no constraints. This solves many of the hard conceptual problems of quantum gravity. It also appears as a useful tool in some numerical simulations of interest in classical relativity. We outline some of the salient aspects and results of this new framework.

8 pages, one figure, fifth prize of the Gravity Research Foundation 2005 essay competition

References in corpus (4)

• Realistic clocks, universal decoherence and the black hole information paradox
• Optimal Constraint Projection for Hyperbolic Evolution Systems
• Consistent discretization and loop quantum geometry
• Fundamental gravitational limitations to quantum computing

Cited by in corpus (10)

• On the regularization ambiguities in loop quantum gravity
• From covariant to canonical formulations of discrete gravity
• Canonical simplicial gravity
• Uniform discretizations: a new approach for the quantization of totally constrained systems
• Discretisations, Constraints and Diffeomorphisms in Quantum Gravity
• Diffeomorphism symmetry in quantum gravity models
• Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
• Canonical linearized Regge Calculus: counting lattice gravitons with Pachner moves
• Uniform discretizations: a quantization procedure for totally constrained systems including gravity
• The SL(2,R) totally constrained model: three quantization approaches