QUANTUM GRAVITY Edited by Rodrigo Sobreiro QUANTUM GRAVITY Edited by Rodrigo Sobreiro Quantum Gravity Edited by Rodrigo Sobreiro Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2012 InTech All chapters are Open Access distributed under the Creative Commons Attribution 3.0 license, which allows users to download, copy and build upon published articles even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. As for readers, this license allows users to download, copy and build upon published chapters even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. Notice Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Daria Nahtigal Technical Editor Teodora Smiljanic Cover Designer InTech Design Team First published February, 2012 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from
[email protected] Quantum Gravity, Edited by Rodrigo Sobreiro p. cm. ISBN 978-953-51-0089-8 Contents Preface VII Chapter 1 Anomalous Gravitational Vacuum Fluctuations Which Act as Virtual Oscillating Dipoles 1 Giovanni Modanese Chapter 2 Planck Scale Cosmology and Asymptotic Safety in Resummed Quantum Gravity: An Estimate of B.F.L. Ward Chapter 3 S-Duality in Topological Supergravity 37 Eckehard W. Mielke and Alí A. Rincón Maggiolo Chapter 4 Quantum Gravity Insights 4 from Smooth 4-Geometries on Trivial 53 Jerzy Król Chapter 5 Fiber Bundles, Gauge Theories and Gravity Rodrigo F. Sobreiro 79 Chapter 6 Quantum Gravity in Cantorian Space-Time L. Marek-Crnjac 87 27 Preface The fundamental Physics of the 20th century was constructed basically from two main theories, general relativity and quantum theory. The later allowed the construction of the standard model which describes three of the four known fundamental interactions in Nature, the exception being the gravity interaction. Unfortunately, general relativity and quantum theory have not been unified into a single coherent description of gravity in the microscopic level yet. The gravity quantization problem exists for almost one century and the final answer is yet unknown. Quantum gravity can then be considered as one of the major problems in fundamental Physics. Many techniques to deal with the quantum nature of gravity have been developed during the last century. For instance, we can name the following techniques, popular among physicists: Canonical quantization, higher derivative gravity, Palatini-Cartan formalisms, gauge theories of the Einstein-Cartan type, Metric-affine gravities and, perhaps the most popular, the string theory. In addition to the above mentioned techniques, one can also refer to loop quantum gr