Quantum Gravity

1. Front Matter

   Pages i-xvi

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2. Quantum Gravity — A Short Overview

   • Claus Kiefer

   Pages 1-13

3. The Search for Quantum Gravity Effects

   • Claus Lämmerzahl

   Pages 15-39

4. Time Paradox in Quantum Gravity

   • Alfredo Macías, Hernando Quevedo

   Pages 41-60

5. Differential Geometry in Non-Commutative Worlds

   • Louis H. Kauffman

   Pages 61-75

6. Algebraic Approach to Quantum Gravity III: Non-Commmutative Riemannian Geometry

   • S. Majid

   Pages 77-100

7. Quantum Gravity as a Quantum Field Theory of Simplicial Geometry

   • Daniele Oriti

   Pages 101-126

8. An Essay on the Spectral Action and its Relation to Quantum Gravity

   • Mario Paschke

   Pages 127-150

9. Towards a Background Independent Formulation of Perturbative Quantum Gravity

   • Romeo Brunetti, Klaus Fredenhagen

   Pages 151-159

10. Mapping-Class Groups of 3-Manifolds in Canonical Quantum Gravity

    • Domenico Giulini

    Pages 161-201

11. Kinematical Uniqueness of Loop Quantum Gravity

    • Christian Fleischhack

    Pages 203-219

12. Topological Quantum Field Theory as Topological Quantum Gravity

    • Kishore Marathe

    Pages 221-235

13. Strings, Higher Curvature Corrections, and Black Holes

    • Thomas Mohaupt

    Pages 237-262

14. The Principle of the Fermionic Projector: An Approach for Quantum Gravity?

    • Felix Finster

    Pages 263-281

15. Gravitational Waves and Energy Momentum Quanta

    • T. Dereli, R. W. Tucker

    Pages 283-292

16. Asymptotic Safety in Quantum Einstein Gravity: Nonperturbative Renormalizability and Fractal Spacetime Structure

    • Oliver Lauscher, Martin Reuter

    Pages 293-313

17. Noncommutative QFT and Renormalization

    • Harald Grosse, Raimar Wulkenhaar

    Pages 315-326

18. Back Matter

    Pages 327-336

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This Edited Volume is based on a workshop on “Mathematical and Physical - pects of Quantum Gravity” held at the Heinrich-Fabri Institute in Blaubeuren st (Germany) from July 28th to August 1 , 2005. This workshop was the succ- sor of a similar workshop held at the same place in September 2003 on the issue of “Mathematical and Physical Aspects of Quantum Field Theories”. Both wo- shops were intended to bring together mathematicians and physicists to discuss profoundquestionswithin the non-emptyintersectionofmathematics andphysics. The basic idea of this series of workshops is to cover a broad range of di?erent approaches (both mathematical and physical) to a speci?c subject in mathema- cal physics. The series of workshops is intended, in particular, to discuss the basic conceptual ideas behind di?erent mathematical and physical approaches to the subject matter concerned. The workshop on which this volume is based was devoted to what is c- monly regarded as the biggest challenge in mathematical physics: the “quanti- tion of gravity”. The gravitational interaction is known to be very di?erent from the known interactions like, for instance, the electroweak or strong interaction of elementary particles. First of all, to our knowledge, any kind of energy has a gravitational coupling. Second, since Einstein it is widely accepted that gravity is intimately related to the structure of space-time. Both facts have far reaching consequences for any attempt to develop a quantum theory of gravity.

• EFE
• Gravitational Waves
• Gravity
• Noncommutative Geometry
• Quantum Field Theory
• Quantum Gravity
• Theoretical physics

From the reviews:

“Presents a selection of contributions presented at the workshop ‘Mathematical and Physical aspects of Quantum Gravity’ … . presentation of various approaches to quantum gravity in one volume is rather unique and provides reader with an opportunity to compare their advantages and disadvantages. A significant advantage of this volume is that the articles are written in a less technical style, focusing only on major theoretical questions, with many contributions being accessible to non-specialists and thus providing a broad overview of this fascinating field of research.” (Vojtěch Pravda, Applications of Mathematics, Vol. 55 (5), 2010)

• Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany

  Bertfried Fauser, Jürgen Tolksdorf, Eberhard Zeidler

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