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 gravity, spin foam quantum gravity, Euclidean quantum gravity and Horava-Lifshitz gravity as emergent gravity models that may describe quantum gravity. All of those techniques resulted in a massive production of interesting scientific texts.

This book presents a series of selected chapters written by renowned authors with the objective to provide an overview and comparison of the various quantum gravity theories. Each chapter treats gravity and its quantization through known and alternative techniques. The book also describes the mathematical models that have provided a framework for the themes here presented. Due to the authors efforts on writing clear yet concise texts, the reader will find each chapter very elucidative. Moreover, all contributions on this book consist on new relevant results on quantum gravity, which makes *Quantum Gravity* an useful book not only for beginners, but also for specialists of the field.

Finally, I wish to express my acknowledgements to the authors for their kindness on attending my requests regarding the format of each chapter and for the time spent to

### XII Preface

produce an important contribution to the book *Quantum Gravity*. I am also thankful to Ms. Daria Nahtigal for her patience with me and dedication to the book.

February 2012
