Quantum gravity is perhaps the most important open problem in fundamental physics. It is the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this 2004 book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

• General introduction to the conceptual and technical problems of quantum gravity • Complete up-do-date introduction to loop quantum gravity • In-depth discussion of the modification of the notions of space and time required by the new physics

### Contents

Preface; Acknowledgements; Terminology and notation; Part I. Relativistic Foundations: 1. General ideas and heuristic picture; 2. General relativity; 3. Mechanics; 4. Hamiltonian general relativity; 5. Quantum mechanics; Part II. Loop Quantum Gravity: 6. Quantum space; 7. Dynamics and matter; 8. Applications; 9. Quantum spacetime: spinfoams; 10. Conclusion; Part III. Appendices: References; Index.

### Reviews

'In spite of its sociological success string theory is still far from a solution of the problem of quantum gravity which should be considered as wide open. The book of Carlo Rovelli provides the basis, both at the technical and the conceptual level, for research in this fundamental problem of physics. The basic issues are clearly and deeply analyzed without any dogmatic stand and with great freedom of thoughts resulting in an invaluable opportunity to learn and think for both mathematicians and physicists.' Alain Connes, Collège de France, I.H.E.S. and Vanderbilt University

'This is a truly great book! … a must for someone interested in quantum gravity.' Mathematical Reviews

'… written very carefully and can be recommended highly to anybody interested in the broad field and in conceptual issues of quantum gravity … experts … will find many new and clear notes of the author's view of loop quantum gravity as one of its founders … a non-expert reader, after working through the book, will be well prepared to read up further details in research or review articles …' General Relativity and Gravitation Journal