Canonical Gravity

Author : Martin Bojowald
Publisher : Cambridge University Press
Page : 313 pages
File Size : 53,9 Mb
Release : 2010-12-23
Category : Science
ISBN : 9781139494137

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Canonical Gravity and Applications by Martin Bojowald Pdf

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.

Author : Abhay Ashtekar
Publisher : World Scientific
Page : 356 pages
File Size : 42,5 Mb
Release : 1991-07-03
Category : Science
ISBN : 9789814571098

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Lectures On Non-perturbative Canonical Gravity by Abhay Ashtekar Pdf

Notes prepared in Collaboration with Ranjeet S Tate It is now generally recognized that perturbative field theoretical methods that have been highly successful in the quantum description of non-gravitational interactions cannot be used as a means of constructing a quantum theory of gravity. The primary aim of the book is to present an up- to-date account of a non-perturbative, canonical quantization program for gravity. Many of the technical results obtained in the process are of interest also to differential geometry, classical general relativity and QCD. The program as a whole was highlighted in virtually every major conference in gravitational physics over the past three years.

Author : Jürgen Ehlers,Helmut Friedrich
Publisher : Springer
Page : 392 pages
File Size : 42,9 Mb
Release : 1994
Category : Science
ISBN : UOM:39015033065072

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Canonical Gravity by Jürgen Ehlers,Helmut Friedrich Pdf

Author : Abhay Ashtekar
Publisher : Unknown
Page : 352 pages
File Size : 47,9 Mb
Release : 1988
Category : Science
ISBN : STANFORD:36105030635366

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New Perspectives in Canonical Gravity by Abhay Ashtekar Pdf

Author : Francesco Cianfrani,Orchidea Maria Lecian,Matteo Lulli,Giovanni Montani
Publisher : World Scientific Publishing Company Incorporated
Page : 300 pages
File Size : 54,6 Mb
Release : 2014
Category : Science
ISBN : 9814556645

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Canonical Quantum Gravity by Francesco Cianfrani,Orchidea Maria Lecian,Matteo Lulli,Giovanni Montani Pdf

This book aims to present a pedagogical and self-consistent treatment of the canonical approach to Quantum Gravity, starting from its original formulation to the most recent developments in the field. We start with an innovative and enlightening introduction to the formalism and concepts on which General Relativity has been built, giving all the information necessary in the later analysis. A brief sketch of the Standard Cosmological Model describing the Universe evolution is also given alongside the analysis of the inflationary mechanism. After deepening the fundamental properties of constrained dynamic systems, the Lagrangian approach to the Einsteinian Theory is presented in some detail, underlining the parallelism with non-Abelian gauge theories. Then, the basic concepts of the canonical approach to Quantum Mechanics are provided, focusing on all those formulations which are relevant for the Canonical Quantum Gravity problem. The Hamiltonian formulation of General Relativity and its constrained structure is then analyzed by comparing different formulations. The resulting quantum dynamics, described by the Wheeler-DeWitt equation, is fully discussed in order to outline its merits and limits. Afterwards, the reformulation of Canonical Quantum Gravity in terms of the Ashtekar-Barbero-Immirzi variables is faced by a detailed discussion of the resulting Loop Quantum Gravity Theory. Finally, we provide a consistent picture of canonical Quantum Cosmology by facing the main features of the Wheeler-DeWitt equation for the homogeneous Bianchi models and then by a detailed treatment of Loop Quantum Cosmology, including very recent developments.

Author : Thomas Thiemann
Publisher : Cambridge University Press
Page : 739 pages
File Size : 55,7 Mb
Release : 2008-11-13
Category : Science
ISBN : 9781139467599

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Modern Canonical Quantum General Relativity by Thomas Thiemann Pdf

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 : Francesco Cianfrani,Orchidea Maria Lecian,Matteo Lulli,Giovanni Montani
Publisher : World Scientific
Page : 324 pages
File Size : 53,5 Mb
Release : 2014-05-21
Category : Science
ISBN : 9789814556668

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Canonical Quantum Gravity by Francesco Cianfrani,Orchidea Maria Lecian,Matteo Lulli,Giovanni Montani Pdf

This book aims to present a pedagogical and self-consistent treatment of the canonical approach to Quantum Gravity, starting from its original formulation to the most recent developments in the field. We start with an innovative and enlightening introduction to the formalism and concepts on which General Relativity has been built, giving all the information necessary in the later analysis. A brief sketch of the Standard Cosmological Model describing the Universe evolution is also given alongside the analysis of the inflationary mechanism. After deepening the fundamental properties of constrained dynamic systems, the Lagrangian approach to the Einsteinian Theory is presented in some detail, underlining the parallelism with non-Abelian gauge theories. Then, the basic concepts of the canonical approach to Quantum Mechanics are provided, focusing on all those formulations which are relevant for the Canonical Quantum Gravity problem. The Hamiltonian formulation of General Relativity and its constrained structure is then analyzed by comparing different formulations. The resulting quantum dynamics, described by the Wheeler–DeWitt equation, is fully discussed in order to outline its merits and limits. Afterwards, the reformulation of Canonical Quantum Gravity in terms of the Ashtekar–Barbero–Immirzi variables is faced by a detailed discussion of the resulting Loop Quantum Gravity Theory. Finally, we provide a consistent picture of canonical Quantum Cosmology by facing the main features of the Wheeler–DeWitt equation for the homogeneous Bianchi models and then by a detailed treatment of Loop Quantum Cosmology, including very recent developments. Contents:Introduction to General RelativityElements of CosmologyConstrained Hamiltonian SystemsLagrangian FormulationsQuantization MethodsQuantum GeometrodynamicsGravity as a Gauge TheoryLoop Quantum GravityQuantum Cosmology Readership: Researchers in theoretical physics, quantum physics, general relativity and astrophysics. Keywords:Canonical Quantum Gravity;Quantum Gravity;Loop Quantum Gravity Theory;General RelativityKey Features:An independent and sound analysis touching many crucial points in the attempt toward a consistent Canonical Quantum Gravity theoryA pedagogical and exhaustive review of fundamental concepts of Quantum Mechanics and General RelativityA solid introduction to Hamiltonian constrained systems with a detailed analysis of the notion of canonical transformation in this class of systems with some concrete examples giving useful insightA self-consistent derivation of the Loop Quantum Gravity Approach, outlining the main progresses and the shortcomings of this theory

Author : Daniele Malafarina
Publisher : Springer Nature
Page : 378 pages
File Size : 53,6 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789819711727

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New Frontiers in Gravitational Collapse and Spacetime Singularities by Daniele Malafarina Pdf

Author : Claus Gerhardt
Publisher : Springer
Page : 200 pages
File Size : 43,9 Mb
Release : 2018-04-14
Category : Science
ISBN : 9783319773711

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The Quantization of Gravity by Claus Gerhardt Pdf

​A unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Standard Model combines electro-magnetism, the strong force and the weak force, but ignores gravity. The quantization of gravity is therefore a necessary first step to achieve a unified quantum theory. In this monograph a canonical quantization of gravity has been achieved by quantizing a geometric evolution equation resulting in a gravitational wave equation in a globally hyperbolic spacetime. Applying the technique of separation of variables we obtain eigenvalue problems for temporal and spatial self-adjoint operators where the temporal operator has a pure point spectrum with eigenvalues $\lambda_i$ and related eigenfunctions, while, for the spatial operator, it is possible to find corresponding eigendistributions for each of the eigenvalues $\lambda_i$, if the Cauchy hypersurface is asymptotically Euclidean or if the quantized spacetime is a black hole with a negative cosmological constant. The hyperbolic equation then has a sequence of smooth solutions which are products of temporal eigenfunctions and spatial eigendistributions. Due to this "spectral resolution" of the wave equation quantum statistics can also be applied to the quantized systems. These quantum statistical results could help to explain the nature of dark matter and dark energy.

Author : B. R. Iyer
Publisher : CUP Archive
Page : 474 pages
File Size : 49,7 Mb
Release : 1988
Category : Science
ISBN : 0521361257

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Highlights in Gravitation and Cosmology by B. R. Iyer Pdf

Author : Steven Carlip,Steven Jonathan Carlip
Publisher : Cambridge University Press
Page : 296 pages
File Size : 40,8 Mb
Release : 2003-12-04
Category : Science
ISBN : 0521545889

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Quantum Gravity in 2+1 Dimensions by Steven Carlip,Steven Jonathan Carlip Pdf

The first comprehensive survey of (2+1)-dimensional quantum gravity - for graduate students and researchers.

Author : Jürgen Ehlers
Publisher : Springer
Page : 367 pages
File Size : 54,9 Mb
Release : 1994-01-01
Category : Electronic books
ISBN : 3540583394

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Canonical Gravity by Jürgen Ehlers Pdf

The search for a quantum gravity theory, a theory expected to combine the principles of general relativity and quantum theory, has led to some of the most deepest and most difficult conceptual and mathematical questions of modern physics. The present book, addressing these issues in the framework of recent versions of canonical quantization, is the first to present coherently the background for their understanding. Starting with an analysis of the structure of constrained systems and the problems of their quantization, it discusses the canonical formulation of classical relativity from different perspectives and leads to recent applications of canonical methods to create a quantum theory of gravity. The book aims to make accessible the most fundamental problems and to stimulate work in this field.

Author : Jürgen Ehlers,Helmut Friedrich
Publisher : Springer
Page : 372 pages
File Size : 49,8 Mb
Release : 2014-03-12
Category : Science
ISBN : 3662139537

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Canonical Gravity: From Classical to Quantum by Jürgen Ehlers,Helmut Friedrich Pdf

The search for a quantum gravity theory, a theory expected to combine the principles of general relativity and quantum theory, has led to some of the most deepest and most difficult conceptual and mathematical questions of modern physics. The present book, addressing these issues in the framework of recent versions of canonical quantization, is the first to present coherently the background for their understanding. Starting with an analysis of the structure of constrained systems and the problems of their quantization, it discusses the canonical formulation of classical relativity from different perspectives and leads to recent applications of canonical methods to create a quantum theory of gravity. The book aims to make accessible the most fundamental problems and to stimulate work in this field.

Author : Jürgen Ehlers,Helmut Friedrich
Publisher : Springer
Page : 392 pages
File Size : 44,6 Mb
Release : 1994
Category : Science
ISBN : UOM:39015033065072

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Canonical Gravity by Jürgen Ehlers,Helmut Friedrich Pdf

Author : Claus Kiefer
Publisher : OUP Oxford
Page : 408 pages
File Size : 43,7 Mb
Release : 2012-04-05
Category : Science
ISBN : 9780191628856

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Quantum Gravity by Claus Kiefer Pdf

The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction — the direct quantisation of Einstein's general theory of relativity and string theory — are covered. Whereas the first attempts to construct a viable theory for the gravitational field alone, string theory assumes that a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantization of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is a detailed presentation of the main approaches employed in quantum general relativity: path-integral quantization, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of string theory centres around its quantum-gravitational aspects and the comparison with quantum general relativity. Physical applications discussed at length include the quantization of black holes, quantum cosmology, the indications of a discrete structure of spacetime, and the origin of irreversibility. This third edition contains new chapters or sections on quantum gravity phenomenology, Horava-Lifshitz quantum gravity, analogue gravity, the holographic principle, and affine quantum gravity. It will present updates on loop quantum cosmology, the LTB model, asymptotic safety, and various discrete approaches. The third edition also contains pedagogical extensions throughout the text. This book will be of interest to researchers and students working in relativity and gravitation, cosmology, quantum field theory and related topics. It will also be of interest to mathematicians and philosophers of science.