Discretisations, Constraints and Diffeomorphisms in Quantum Gravity

Abstract

In this review we discuss the interplay between discretization, constraint implementation, and diffeomorphism symmetry in Loop Quantum Gravity and Spin Foam models. To this end we review the Consistent Discretizations approach, which is an application of the master constraint program to construct the physical Hilbert space of the canonical theory, as well as the Perfect Actions approach, which aims at finding a path integral measure with the correct symmetry behavior under diffeomorphisms.

Contribution for a special issue of SIGMA on Loop Quantum Gravity and Cosmology

References in corpus (15)

• The Ponzano-Regge model
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• The Semiclassical Limit of Causal Dynamical Triangulations
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• Canonical simplicial gravity
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• Discrete space-time
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Cited by in corpus (17)

• Numerical evidence for a phase transition in 4d spin foam quantum gravity
• From the discrete to the continuous - towards a cylindrically consistent dynamics
• SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry
• Path integral measure and triangulation independence in discrete gravity
• Canonical simplicial gravity
• Time evolution as refining, coarse graining and entangling
• Canonical tensor models with local time
• Constraint analysis for variational discrete systems
• Quantization of systems with temporally varying discretization II: Local evolution moves
• Quantization of systems with temporally varying discretization I: Evolving Hilbert spaces
• Projective Limits of State Spaces I. Classical Formalism
• Chaos, Dirac observables and constraint quantization
• Challenges for Emergent Gravity
• Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
• Canonical linearized Regge Calculus: counting lattice gravitons with Pachner moves
• Classification of constraints and degrees of freedom for quadratic discrete actions
• A Noether Theorem for discrete Covariant Mechanics