Quantum gravity : mathematical models and experimental bounds

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. This book provides the reader with an overview of the different mathematical attempts to quantize gravity written by leading experts in this field. Also discussed are the possible experimental bounds on quantum gravity effects. All of the contributions have been strictly refereed. The present volume emerged from the 2nd Blaubeuren Workshop "Mathematical and Physical Aspects of Quantum Gravity''. In general, these Workshops are intended to bring together experts in mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics. Quantum Gravity -- A Short Overview / Claus Kiefer -- The Search For Quantum Gravity / Claus Lammerzahl -- Time Paradox In Quantum Gravity / Alfredo Macias And Hernando Quevedo -- Differential Geometry In Non-commutative Worlds / Louis H. Kauffman -- Algebraic Approach To Quantum Gravity Iii : Non-commutative Riemannian Geometry / Shahn Majid -- Quantum Gravity As A Quantum Field Theory Of Simplicial Geometry / Daniele Oriti -- An Essay On The Spectral Action And Its Relation To Quantum Gravity / Mario Paschke -- Towards A Background Independent Formulation Of Perturbative Quantum Gravity / Romeo Brunetti And Klaus Fredenhagen -- Mapping-class Groups Of 3-manifolds / Domenico Giulini -- Kinematical Uniqueness Of Loop Quantum Gravity / Christian Fleischhack -- Topological Quantum Field Theory As Topological Quantum Gravity / Kishore Marathe -- Strings, Higher Curvature Corrections, And Black Holes / Thomas Mohaupt -- The Principle Of The Fermionic Projector : An Approach For Quantum Gravity? / Felix Finster -- Gravitational Waves And Energy Momentum Quanta / Tekin Dereli And Robin W. Tucker -- Asymptotic Safety In Quantum Einstein Gravity : Nonperturbative Renormalizability And Fractal Spacetime Structure / Oliver Lauscher And Martin Renter -- Noncommutative Qft And Renormalization / Harold Grosse And Raimar Wulkenhaar. Bertfried Fauser, Jürgen Tolksdorf, Eberhard Zeidler, Editors. This Edited Volume Is Based On A Workshop On 'mathematical And Physical Aspects Of Quantum Gravity', Held At The Heinrich-fabri Institute In Blaubeuren (germany) From July 28th To August 1st, 2005--preface. Includes Bibliographical References And Index. 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 This book provides the reader with an overview of the different mathematical attempts to quantize gravity written by leading experts in this field. Also discussed are the possible experimental bounds on quantum gravity effects. The contributions have been strictly refereed and are written in an accessible style. The present volume emerged from the 2nd Blaubeuren Workshop "Mathematical and Physical Aspects of Quantum Gravity".