Living Reviews in Relativity

"Loop Quantum Gravity"
Carlo Rovelli  

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1 Introduction
2 Quantum Gravity: Where Are We?
2.1 What is the problem? The view of a high-energy physicist
2.2 What is the problem? The view of a relativist
2.3 Strings and loops
3 The Development of Loop Gravity
4 Resources
5 Ideas and Physical Inputs
5.1 Quantum field theory on a differentiable manifold
5.2 Why loops?
5.3 Physical meaning of diffeomorphism invariance and its implementation in the quantum theory
5.4 Problems not addressed
6 Formalism
6.1 Classical theory
6.2 Quantum kinematics
6.3 Loop and spin network states
6.4 Diffeomorphism invariance
6.5 Other structures in ℋ
6.6 Dynamics: I. Hamiltonian
6.7 Dynamics: II. Spin foams
6.8 Dynamics: III. Group field theory
6.9 Matter couplings
6.10 Variants: fundamental discreteness
7 Physical Results
8 Open Problems and Current Lines of Investigation
9 Short Summary and Conclusion
10 Acknowledgments
Open References References