Includes bibliographical references (pages 383-391) and index.
Introduction -- Conformal field theory in Minkowski space -- Conformal field theory in Euclidean space -- Basis of two-dimensional conformal field theory -- Conformal anomaly and Wess-Zumino action -- Two-dimensional quantum gravity -- Background-free quantum gravity -- Physical states of quantum gravity -- Gravitational counterterms and conformal anomalies -- Renomalization in quantum gravity -- The universe in Einstein gravity -- Quantum gravity cosmology -- Cosmological perturbation theory -- From quantum gravity to CMB -- Appendix A: Useful gravitational formulas -- Appendix B : Addenda to conformal field theory -- Appendix C : Useful functions on three-sphere -- Appendix D : Addenda to renormalization theory -- Appendix E : Addenda to cosmology.
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"What is the world beyond the Planck scale that provides the minimum unit of the universe? The goal of quantum gravity is to reveal physical laws in such a world. There, quantum fluctuations of gravity become large, and what is called a background-free world where the concept of time and distance is lost shall be realized. The renormalizable quantum gravity introduced in this book offers a theory in which such a world is described by a certain conformal field theory and a deviation from there is handled as a perturbation. This is the state-of-the-art of modern physics that will help in understanding the history of the universe, from its birth to the present." -- Back cover.