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
Summary
The construction of a quantum theory of gravity is the most fundamental challenge confronting contemporary theoretical physics. The different physical ideas which evolved while developing a theory of quantum gravity require highly advanced mathematical methods. This book presents different mathematical approaches to formulate a theory of quantum gravity. It represents a carefully selected cross-section of lively discussions about the issue of quantum gravity which took place at the second workshop "Mathematical and Physical Aspects of Quantum Gravity" in Blaubeuren, Germany. This collection covers in a unique way aspects of various competing approaches. A unique feature of the book is the presentation of different approaches to quantum gravity making comparison feasible. This feature is supported by an extensive index. The book is mainly addressed to mathematicians and physicists who are interested in questions related to mathematical physics. It allows the reader to obtain a broad and up-to-date overview on a fascinating active research area
