This volume presents different approaches to quantum gravity, including loop quantum gravity, string theory, noncommutative geometry, canonical quantum gravity, and more advanced approaches. Coverage includes a discussion of the recent experimental status of the search for quantum gravity effects and is accessible to non-experts in the field. Extensive indexing of all articles ensures accessibility to keywords and phrases. The construction of a quantum theory of gravity is the most fundamental challenge confronting contemporary theoretical physics. The different physical ideas evolved in developing a theory of quantum gravity require highly advanced mathematical methods. Written by leading experts in this field, this book provides the reader with an overview of the different mathematical attempts to quantize gravity.

Autorentext
Prof. Dr. Dr. h.c. Eberhard Zeidler works at the Max Planck Institute for Mathematics in the Sciences in Leipzig (Germany). In 1996 he was one of the founding directors of this institute. He is a member of the Academy of Natural Scientists Leopoldina. In 2006 he was awarded the 'Alfried Krupp Wissenschaftspreis' of the Alfried Krupp von Bohlen und Halbach-Stiftung.

Inhalt
Quantum Gravity A Short Overview.- The Search for Quantum Gravity Effects.- Time Paradox in Quantum Gravity.- Differential Geometry in Non-Commutative Worlds.- Algebraic Approach to Quantum Gravity III: Non-Commmutative Riemannian Geometry.- Quantum Gravity as a Quantum Field Theory of Simplicial Geometry.- An Essay on the Spectral Action and its Relation to Quantum Gravity.- Towards a Background Independent Formulation of Perturbative Quantum Gravity.- Mapping-Class Groups of 3-Manifolds in Canonical Quantum Gravity.- Kinematical Uniqueness of Loop Quantum Gravity.- Topological Quantum Field Theory as Topological Quantum Gravity.- Strings, Higher Curvature Corrections, and Black Holes.- The Principle of the Fermionic Projector: An Approach for Quantum Gravity?.- Gravitational Waves and Energy Momentum Quanta.- Asymptotic Safety in Quantum Einstein Gravity: Nonperturbative Renormalizability and Fractal Spacetime Structure.- Noncommutative QFT and Renormalization.