Martin Bojowald - Böcker

Canonical methods are a powerful mathematical tool within the field of gravitational research, both theoretical and experimental, and have contributed to a number of recent developments in physics. Providing mathematical foundations as well as physical applications, this is the first systematic explanation of canonical methods in gravity. The book discusses the mathematical and geometrical notions underlying canonical tools, highlighting their applications in all aspects of gravitational research from advanced mathematical foundations to modern applications in cosmology and black hole physics. The main canonical formulations, including the Arnowitt-Deser-Misner (ADM) formalism and Ashtekar variables, are derived and discussed. Ideal for both graduate students and researchers, this book provides a link between standard introductions to general relativity and advanced expositions of black hole physics, theoretical cosmology or quantum gravity.

Fundamental Physics: A Guide to Relativity and Quantum Physics presents the two foundational pillars of modern physics, quantum mechanics and general relativity, in a coherent form aimed primarily at upper-level undergraduate students. It provides a unified picture of the underlying field of mathematical physics and the fruitful interactions between different methods and applications. To help students navigate both topics, the book takes a systematic, pedagogical and uniform approach to the underlying theories and applications. This includes detailed discussions of applications, such as in atomic and particle physics, measurements of space and time, black holes and cosmology.The book is essential for upper-level undergraduate students looking to develop a cohesive understanding of the ways in which quantum mechanics and general relativity are central not only to the challenges and approaches to quantum theories of gravity, but also to gravitational implications on sensitive quantum effects. Worked examples and homework problems are available throughout.Key Features:• Class tested textbook combines two fundamental topics in modern physics: quantum mechanics and general relativity.• Detailed conceptual discussions of physics insights are combined with careful mathematical constructions. • Worked examples are available throughout.• Chapter-end homework problems are also included.

Consequences of quantum gravity on grander scales are expected to be enormous: only such a theory can show how black holes really behave and where our universe came from. Applications of loop quantum gravity to cosmology have especially by now shed much light on cosmic evolution of a universe in a fundamental, microscopic description. Modern techniques are explained in this book which demonstrate how the universe could have come from a non-singular phase before the big bang, how equations for the evolution of structure can be derived, but also what fundamental limitations remain to our knowledge of the universe before the big bang.The following topics will be covered in this book:Hamiltonian cosmology: a general basic treatment of isotropy, perturbations and their role for observations; useful in general cosmology.Effective equations: an efficient way to evaluate equations of quantum gravity, which is also useful in other areas of physics where quantum theory is involved.Loop quantization: a new formalism for the atomic picture of space-time; usually presented at a sophisticated mathematical level, but evaluated here from an intuitive physical side.The book will start with physical motivations, rather than mathematical developments which is more common in other expositions of this field. All the required mathematical methods will be presented, but will not distract the reader from seeing the underlying physics. Simple but representative models will be presented first to show the basic features, which are then used to work upwards to a general description of quantum gravity and its applications in cosmology. This will make the book accessible to a more general physics readership.

Consequences of quantum gravity on grander scales are expected to be enormous: only such a theory can show how black holes really behave and where our universe came from. Applications of loop quantum gravity to cosmology have especially by now shed much light on cosmic evolution of a universe in a fundamental, microscopic description. Modern techniques are explained in this book which demonstrate how the universe could have come from a non-singular phase before the big bang, how equations for the evolution of structure can be derived, but also what fundamental limitations remain to our knowledge of the universe before the big bang.The following topics will be covered in this book:Hamiltonian cosmology: a general basic treatment of isotropy, perturbations and their role for observations; useful in general cosmology.Effective equations: an efficient way to evaluate equations of quantum gravity, which is also useful in other areas of physics where quantum theory is involved.Loop quantization: a new formalism for the atomic picture of space-time; usually presented at a sophisticated mathematical level, but evaluated here from an intuitive physical side.The book will start with physical motivations, rather than mathematical developments which is more common in other expositions of this field. All the required mathematical methods will be presented, but will not distract the reader from seeing the underlying physics. Simple but representative models will be presented first to show the basic features, which are then used to work upwards to a general description of quantum gravity and its applications in cosmology. This will make the book accessible to a more general physics readership.