Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 017, 30 pages      arXiv:1109.0740      https://doi.org/10.3842/SIGMA.2012.017
Contribution to the Special Issue “Loop Quantum Gravity and Cosmology”

Relational Observables in Gravity: a Review

Johannes Tambornino
Laboratoire de Physique, ENS Lyon, CNRS-UMR 5672, 46 Allée d'Italie, Lyon 69007, France

Received August 31, 2011, in final form March 14, 2012; Published online March 28, 2012

Abstract
We present an overview on relational observables in gravity mainly from a loop quantum gravity perspective. The gauge group of general relativity is the diffeomorphism group of the underlying manifold. Consequently, general relativity is a totally constrained theory with vanishing canonical Hamiltonian. This fact, often referred to as the problem of time, provides the main conceptual difficulty towards the construction of gauge-invariant local observables. Nevertheless, within the framework of complete observables, that encode relations between dynamical fields, progress has been made during the last 20 years. Although analytic control over observables for full gravity is still lacking, perturbative calculations have been performed and within de-parameterizable toy models it was possible for the first time to construct a full set of gauge invariant observables for a background independent field theory. We review these developments and comment on their implications for quantum gravity.

Key words: Dirac observables; quantum gravity; problem of time; gauge invariance.

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