The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spacetime cannot be fundamentally correct. Hence there should exist a broader theory comprising both in appropriate limits, i.e., quantum gravity. This book gives readers a comprehensive introduction accessible to interested non-experts to the main issues surrounding the search for quantum gravity. These issues relate to fundamental questions concerning the various formalisms of quantization; specific questions concerning concrete processes, like gravitational collapse or black-hole evaporation; and the all important question concerning the possibility of experimental tests of quantum-gravity effects.

A unique description of the phenomena that arise from the interaction between quantum systems and their environment. Because of the novel character of the approach discussed, the book addresses scientists from all fields of physics and related disciplines as well as students of physics.

General relativity ranks among the most accurately tested fundamental theories in all of physics. Deficiencies in mathematical and conceptual understanding still exist, hampering further progress. This book collects surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods.

General relativity ranks among the most accurately tested fundamental theories in all of physics. Deficiencies in mathematical and conceptual understanding still exist, hampering further progress. This book collects surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods.

The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spacetime cannot be fundamentally correct. Hence there should exist a broader theory comprising both in appropriate limits, i.e., quantum gravity. This book gives readers a comprehensive introduction accessible to interested non-experts to the main issues surrounding the search for quantum gravity. These issues relate to fundamental questions concerning the various formalisms of quantization; specific questions concerning concrete processes, like gravitational collapse or black-hole evaporation; and the all important question concerning the possibility of experimental tests of quantum-gravity effects.

This book describes the phenomena that arise from the interaction between quantum systems and their environment. Since the first edition appeared in 1996, the concepts of decoherence have become firmly established experimentally and are now widely used in the literature. The major consequences of decoherence are the emergence of "classicality", superselection rules, the border line between microscopic and macroscopic behavior, the emergence of classical spacetime, and the appearance of quantum jumps. Most of the new developments in this rapidly evolving field are discussed in this second edition: chaos theory, quantum information, neuroscience, primordial fluctuations in cosmology, black holes and string theory, experimental tests, and interpretational issues. While the major part of the book is concerned with environmental decoherence derived from a universal Schrödinger equation, later chapters address complementary or competing approaches, such as consistent histories, open system dynamics, algebraic methods, and collapse models.