Loop Quantum Gravity and the Meaning of Diffeomorphism Invariance

Abstract

This series of lectures gives a simple and self-contained introduction to the non-perturbative and background independent loop approach of canonical quantum gravity. The Hilbert space of kinematical quantum states is constructed and a complete basis of spin network states is introduced. An application of the formalism is provided by the spectral analysis of the area operator, which is the quantum analogue of the classical area function. This leads to one of the key results of loop quantum gravity: the derivation of the discreteness of the geometry and the computation of the quanta of area. Finally, an outlock on a possible covariant formulation of the theory is given leading to a "sum over histories" approach, denoted as spin foam model. Throughout the whole lecture great significance is attached to conceptual and interpretational issues. In particular, special emphasis is given to the role played by the diffeomorphism group and the notion of observability in general relativity.

Lectures given at the 35th Karpacz Winter School on Theoretical Physics: From Cosmology to Quantum Gravity. 52 pages. 17 eps figures

Cited by in corpus (17)

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• Spacetime as a Feynman diagram: the connection formulation
• SU(2) Loop Quantum Gravity seen from Covariant Theory
• Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction
• A spin foam model without bubble divergences
• On the Existence of Spacetime Structure
• Barrett-Crane spin foam model from generalized BF-type action for gravity
• Critical Overview of Loops and Foams
• Deformations of Polyhedra and Polygons by the Unitary Group
• Breaking Diffeomorphism Invariance and Tests for the Emergence of Gravity
• Timelike surfaces in Lorentz covariant loop gravity and spin foam models
• Fisher Metric, Geometric Entanglement and Spin Networks
• Hubble operator in isotropic loop quantum cosmology
• Ghost Equations and Diffeomorphism Invariant Theories
• On the counting of black hole states in loop quantum gravity
• Geometry of spin-field coupling on the worldline
• Proceedings to the 'Euroconference on Symmetries Beyond the Standard Model',12. - 17. July 2003, Portoroz, Slovenia (Part 2 of 2)