Principles Of Quantum General Relativity

Author : Eduard Prugovecki
Publisher : World Scientific
ISBN 13 : 9814501174
Total Pages : 376 pages
Book Rating : 4.70/5 ( download)

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Download or read book Principles of Quantum General Relativity written by Eduard Prugovecki and published by World Scientific. This book was released on 1995-01-20 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents: Survey of Principal Historical DevelopmentsClassical Frame Buddles in General RelativityQuantum Frames and Spacetime LocalizabilityQuantum Geometry over a Classical Base SpacetimeMassive Quantum-Geometic Boson FieldsMassive Quantum-Geometric Fermion FieldsMassless Quantum-Geometric Gauge FieldsQuantum-Geometric Gravity Readership: Theoretical physicists and mathematical physicists. keywords:Quantum Geometry;Quantum Gravity;Quantum-Geometric Fields in Curved Spacetime;Quantum Bundles “The reader gets the impression that the present monograph represents the state of the art in this special discipline of mathematical physics and that new vistas in our understanding of quantum gravity are opened. Valuable résumés after sound mathematical derivations are helpful in understanding the motivation of the author and clarifying his intentions. Therefore, the monograph can be recommended for researchers and those who are interested in the frontiers of the unifying of basic physical phenomena.” B Kämpfer Zeitschrift für Kristallographie

Author : Eduard Prugove?ki
Publisher : World Scientific
ISBN 13 : 9789810221386
Total Pages : 380 pages
Book Rating : 4.8X/5 ( download)

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Download or read book Principles of Quantum General Relativity written by Eduard Prugove?ki and published by World Scientific. This book was released on 1995 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 9789810220778
Total Pages : 351 pages
Book Rating : 4.74/5 ( download)

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Download or read book Principles of Quantum General Relativity written by Eduard Prugovečki and published by World Scientific Publishing Company Incorporated. This book was released on 1995 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 113946759X
Total Pages : 739 pages
Book Rating : 4.99/5 ( download)

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Download or read book Modern Canonical Quantum General Relativity written by Thomas Thiemann and published by Cambridge University Press. This book was released on 2008-11-13 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : M. Sachs
Publisher : Springer Science & Business Media
ISBN 13 : 9789027722478
Total Pages : 254 pages
Book Rating : 4.71/5 ( download)

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Download or read book Quantum Mechanics from General Relativity written by M. Sachs and published by Springer Science & Business Media. This book was released on 1986-09-30 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a sequel to my earlier work, General Relativity and Matter [1], which will be referred to henceforth as GRM. The monograph, GRM, focuses on the full set of implications of General Relativity Theory, as a fundamental theory of matter in all domains, from elementary particle physics to cosmology. It is shown there to exhibit an explicit unification of the gravitational and electromagnetic fields of force with the inertial manifestations of matter, expressing the latter explicitly in terms of a covariant field theory within the structure of this general theory. This monograph will focus, primarily, on the special relativistic limit of the part of this general field theory of matter that deals with inertia, in the domain where quantum mechanics has been evoked in contemporary physics as a funda mental explanation for the behavior of elementary matter. Many of the results presented in this book are based on earlier published works in the journals, which will be listed in the Bibliography. These results will be presented here in an expanded form, with more discussion on the motivation and explanation for the theoretical development of the subject than space would allow in normal journal articles, and they will be presented in one place where there would then be a more unified and coherent explication of the subject.

Author : Margaret Prugovecki
Publisher : Springer Science & Business Media
ISBN 13 : 9401579717
Total Pages : 543 pages
Book Rating : 4.11/5 ( download)

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Download or read book Quantum Geometry written by Margaret Prugovecki and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Edward Anderson
Publisher : Springer
ISBN 13 : 3319588486
Total Pages : 920 pages
Book Rating : 4.83/5 ( download)

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Download or read book The Problem of Time written by Edward Anderson and published by Springer. This book was released on 2017-09-18 with total page 920 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a treatise on time and on background independence in physics. It first considers how time is conceived of in each accepted paradigm of physics: Newtonian, special relativity, quantum mechanics (QM) and general relativity (GR). Substantial differences are moreover uncovered between what is meant by time in QM and in GR. These differences jointly source the Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of the QM and GR paradigms, as is required in particular for a background independent theory of quantum gravity. A sizeable proportion of current quantum gravity programs - e.g. geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense. This book's foundational topic is thus furthermore of practical relevance in the ongoing development of quantum gravity programs. This book shows moreover that eight of the nine facets of the Problem of Time already occur upon entertaining background independence in classical (rather than quantum) physics. By this development, and interpreting shape theory as modelling background independence, this book further establishes background independence as a field of study. Background independent mechanics, as well as minisuperspace (spatially homogeneous) models of GR and perturbations thereabout are used to illustrate these points. As hitherto formulated, the different facets of the Problem of Time greatly interfere with each others' attempted resolutions. This book explains how, none the less, a local resolution of the Problem of Time can be arrived at after various reconceptualizations of the facets and reformulations of their mathematical implementation. Self-contained appendices on mathematical methods for basic and foundational quantum gravity are included. Finally, this book outlines how supergravity is refreshingly different from GR as a realization of background independence, and what background independence entails at the topological level and beyond.

Author : I.L Buchbinder
Publisher : Routledge
ISBN 13 : 1351453823
Total Pages : 239 pages
Book Rating : 4.20/5 ( download)

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Download or read book Effective Action in Quantum Gravity written by I.L Buchbinder and published by Routledge. This book was released on 2017-09-29 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Horst-Heino Borzeszkowski
Publisher : Springer Science & Business Media
ISBN 13 : 9400938934
Total Pages : 140 pages
Book Rating : 4.39/5 ( download)

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Download or read book The Meaning of Quantum Gravity written by Horst-Heino Borzeszkowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Lawrence B. Crowell
Publisher : World Scientific
ISBN 13 : 9812565159
Total Pages : 388 pages
Book Rating : 4.50/5 ( download)

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Download or read book Quantum Fluctuations of Spacetime written by Lawrence B. Crowell and published by World Scientific. This book was released on 2005 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three key aspects of quantum gravity are considered in this book: phenomenology, potential experimental aspects and foundational theory. The phenomenology is the treatment of metric quantum fluctuations as torsional curves that deviate from classical expectations. This leads to possible experimental configurations that may detect such fluctuations. Most of these proposed experiments are quantum optical measurements of subtle quantum gravity effects in the interaction of photons and atoms. The foundational discussions attempt to find an substratum to string theories, which are motivated by the phenomenological treatment. Quantum gravity is not the quantization of general relativity, but is instead the embedding of quantum theory and gravitation into a more fundamental field theoretic framework.