Author: Eduard Prugovecki Publisher: World Scientific ISBN: 9814501174 Category : Science Languages : en Pages : 382
Book Description
This monograph explains and analyzes the principles of a quantum-geometric framework for the unification of general relativity and quantum theory. By taking advantage of recent advances in areas like fibre and superfibre bundle theory, Krein spaces, gauge fields and groups, coherent states, etc., these principles can be consistently incorporated into a framework that can justifiably be said to provide the foundations for a quantum extrapolation of general relativity. This volume aims to present this approach in a way which places as much emphasis on fundamental physical ideas as on their precise mathematical implementation. References are also made to the ideas of Einstein, Bohr, Born, Dirac, Heisenberg and others, in order to set the work presented here in an appropriate historical context.
Author: Eduard Prugove?ki Publisher: World Scientific ISBN: 9789810221386 Category : Science Languages : en Pages : 380
Book Description
This monograph explains and analyzes the principles of a quantum-geometric framework for the unification of general relativity and quantum theory. By taking advantage of recent advances in areas like fibre and superfibre bundle theory, Krein spaces, gauge fields and groups, coherent states, etc., these principles can be consistently incorporated into a framework that can justifiably be said to provide the foundations for a quantum extrapolation of general relativity. This volume aims to present this approach in a way which places as much emphasis on fundamental physical ideas as on their precise mathematical implementation. References are also made to the ideas of Einstein, Bohr, Born, Dirac, Heisenberg and others, in order to set the work presented here in an appropriate historical context.
Author: Eduard Prugovečki Publisher: World Scientific Publishing Company Incorporated ISBN: 9789810220778 Category : Science Languages : en Pages : 351
Book Description
Ch. 1. Survey of principal historical developments. 1.1. From special to general relativity. 1.2. Geometry as part of physical theory. 1.3. Quantum theory and the idea of fundamental length. 1.4. Localizability and renormalizability in quantum field theory. 1.5. Quantum field theory in curved spacetime. 1.6. From canonical quantum gravity to superstrings -- ch. 2. Classical frame bundles in general relativity. 2.1. General covariance under coordinate transformations. 2.2. General covariance and classical frame bundles. 2.3. Moving frames in principal frame bundles. 2.4. Gauge invariance in associated bundles. 2.5. Connections and gauge transformations. 2.6. Levi-Civita connections and the strong equivalence principle. 2.7. The Einstein field equations and canonical gravity -- ch. 3. Quantum frames and spacetime localizability. 3.1. The uncertainty principle and representations of the Galilei group. 3.2. Quantum mechanics and informational completeness. 3.3. Informationally complete nonrelativistic quantum frames. 3.4. Sharp-point limits of nonrelativistic quantum frames. 3.5. Path integration and nonrelativistic quantum frames. 3.6. Poincaré covariance and relativistic quantum localizability. 3.7. Poincaré covariance and quantum Lorentz frames. 3.8. Fundamental special-relativistic quantum Lorentz frames -- ch. 4. Quantum geometry over a classical base spacetime. 4.1. Quantum frame bundles and associated bundles. 4.2. The internal Hilbert structure of quantum bundles. 4.3. Connections on affine frame bundles and associated bundles. 4.4. Connections and parallel transport in quantum bundles. 4.5. Quantum tensorial bundles and quantum metrics. 4.6. Quantum-geometric propagation in quantum bundles. 4.7. The physical meaning of quantum-geometric propagation. 4.8. Relativistic causality of classical and quantum propagation
Author: Thomas Thiemann Publisher: Cambridge University Press ISBN: 113946759X Category : Science Languages : en Pages : 739
Book Description
This book provides a complete treatise of the canonical quantisation of general relativity and the loop quantum gravity theory. Mathematical concepts are provided, so it can be read by graduate students with a basic knowledge of quantum field theory or general relativity.
Author: Dean Rickles Publisher: Oxford University Press ISBN: 0199269696 Category : Mathematics Languages : en Pages : 283
Book Description
What is spacetime? General relativity and quantum field theory answer this question in different ways. This collection of essays looks at the problem of uniting these two fundamental theories of our world, focusing on the nature of space and time within this quantum framework.
Author: Margaret Prugovecki Publisher: Springer Science & Business Media ISBN: 9401579717 Category : Science Languages : en Pages : 543
Book Description
This monograph presents a review and analysis of the main mathematical, physical and epistomological difficulties encountered at the foundational level by all the conventional formulations of relativistic quantum theories, ranging from relativistic quantum mechanics and quantum field theory in Minkowski space, to the various canonical and covariant approaches to quantum gravity. It is, however, primarily devoted to the systematic presentation of a quantum framework meant to deal effectively with these difficulties by reconsidering the foundations of these subjects, analyzing their epistemic nature, and then developing mathematical tools which are specifically designed for the elimination of all the basic inconsistencies. A carefully documented historical survey is included, and additional extensive notes containing quotations from original sources are incorporated at the end of each chapter, so that the reader will be brought up-to-date with the very latest developments in quantum field theory in curved spacetime, quantum gravity and quantum cosmology. The survey further provides a backdrop against which the new foundational and mathematical ideas of the present approach to these subjects can be brought out in sharper relief.
Author: Julian B. Barbour Publisher: Springer Science & Business Media ISBN: 9780817638238 Category : Science Languages : en Pages : 558
Book Description
This volume is a collection of scholarly articles on the Mach Principle, the impact that this theory has had since the end of the 19th century, and its role in helping Einstein formulate the doctrine of general relativity. 20th-century physics is concerned with the concepts of time, space, motion, inertia and gravity. The documentation on all of these makes this book a reference for those who are interested in the history of science and the theory of general relativity
Author: Horst-Heino Borzeszkowski Publisher: Springer Science & Business Media ISBN: 9400938934 Category : Science Languages : en Pages : 140
Book Description
In discussing the question of whether General Relativity Theory really needs to be quantized, a simply negative answer cannot be accepted, of course. Such an answer is not satisfying because, first, Einstein's gravitational equations connect gravity and non-gravitational matter and because, second, it can be taken for granted that non-gravitational matter has an atomic or quantum structure such that its energy-momentum tensor standing on the right-hand side of Einstein's equations is formed out of quantum operators. These two facts make it impossible to read the left-hand side of Einstein's equations as an ordinary classical function. This does not necessarily mean, however, that we must draw the conclusion that General Relativity Theory, similar to electrodynamics, could or should be quantized in a rigorous manner and that this quantization has similar consequences to quantum electrodynamics. In other words, when for reasons of consistency quantization is tried, then one has to ask whether and where the quantization procedure has a physical meaning, i.e., whether there exist measurable effects of quantum gravity. IQ accordance with these questions, we are mainly dealing with the discus sion of the principles of quantized General Relativity Theory and with the estimation of quantum effects including the question of their measurability. This analysis proves that it is impossible to distinguish between classical and quantum General Relativity Theory for the extreme case of Planck's orders of magnitude. In other words, there does not exist a physically meaningful rigorous quantization conception for Einstein's theory.
Author: I.L Buchbinder Publisher: Routledge ISBN: 1351453823 Category : Science Languages : en Pages : 432
Book Description
In part one of Effective Action in Quantum Gravity, the book describes the principles of quantum field theory and the significance of and theory behind effective action. Part two deals with quantum field theory in curved space-time and the effective action. These two parts provide the tools for understanding the rest of the book, which is devoted to selected problems of quantum gravity where the effective action plays a major role. The book assumes only a basic understanding of quantum field theory and general relativity and will be of interest to postgraduate students and researchers in theoretical high-energy physics and gravitational theory.
Author: Eduard Prugovecki
Author: Eduard Prugove?ki
Author: Eduard Prugovečki
Author: Thomas Thiemann
Author: Dean Rickles
Author: Margaret Prugovecki
Author: Julian B. Barbour
Author: Horst-Heino Borzeszkowski
Author: M. A. H. MacCallum
Author: I.L Buchbinder