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Non-Inertial Frames and Dirac Observables in Relativity

Author: Luca Lusanna

Publisher: Cambridge University Press

Published: 2019-07-04

Total Pages: 339

ISBN-13: 110857419X

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Interpreting general relativity relies on a proper description of non-inertial frames and Dirac observables. This book describes global non-inertial frames in special and general relativity. The first part covers special relativity and Minkowski space time, before covering general relativity, globally hyperbolic Einstein space-time, and the application of the 3+1 splitting method to general relativity. The author uses a Hamiltonian description and the Dirac–Bergmann theory of constraints to show that the transition between one non-inertial frame and another is a gauge transformation, extra variables describing the frame are gauge variables, and the measureable matter quantities are gauge invariant Dirac observables. Point particles, fluids and fields are also discussed, including how to treat the problems of relative times in the description of relativistic bound states, and the problem of relativistic centre of mass. Providing a detailed description of mathematical methods, the book is perfect for theoretical physicists, researchers and students working in special and general relativity.

Book Synopsis Non-Inertial Frames and Dirac Observables in Relativity by : Luca Lusanna

Download or read book Non-Inertial Frames and Dirac Observables in Relativity written by Luca Lusanna and published by Cambridge University Press. This book was released on 2019-07-04 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interpreting general relativity relies on a proper description of non-inertial frames and Dirac observables. This book describes global non-inertial frames in special and general relativity. The first part covers special relativity and Minkowski space time, before covering general relativity, globally hyperbolic Einstein space-time, and the application of the 3+1 splitting method to general relativity. The author uses a Hamiltonian description and the Dirac–Bergmann theory of constraints to show that the transition between one non-inertial frame and another is a gauge transformation, extra variables describing the frame are gauge variables, and the measureable matter quantities are gauge invariant Dirac observables. Point particles, fluids and fields are also discussed, including how to treat the problems of relative times in the description of relativistic bound states, and the problem of relativistic centre of mass. Providing a detailed description of mathematical methods, the book is perfect for theoretical physicists, researchers and students working in special and general relativity.

2001: A Relativistic Spacetime Odyssey: Experiments And Theoretical Viewpoints On General Relativity And Quantum Gravity - Proceedings Of The 25th Johns Hopkins Workshop On Current Problems In Particle Theory

Author: Ignazio Ciufolini

Publisher: World Scientific

Published: 2003-01-16

Total Pages: 525

ISBN-13: 9814487988

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This volume offers a comprehensive overview of our understanding of gravity at both the experimental and the theoretical level. Critical reviews by experts cover topics ranging from astrophysics (anisotropies in the cosmic microwave background, gamma ray bursts, neutron stars and astroparticles), cosmology, the status of gravitational wave sources and detectors, verification of Newton's law at short distances, the equivalence principle, gravito-magnetism, measurement theory, time machines and the foundations of Einstein's theory, to string theory and loop quantum gravity.

Book Synopsis 2001: A Relativistic Spacetime Odyssey: Experiments And Theoretical Viewpoints On General Relativity And Quantum Gravity - Proceedings Of The 25th Johns Hopkins Workshop On Current Problems In Particle Theory by : Ignazio Ciufolini

Download or read book 2001: A Relativistic Spacetime Odyssey: Experiments And Theoretical Viewpoints On General Relativity And Quantum Gravity - Proceedings Of The 25th Johns Hopkins Workshop On Current Problems In Particle Theory written by Ignazio Ciufolini and published by World Scientific. This book was released on 2003-01-16 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a comprehensive overview of our understanding of gravity at both the experimental and the theoretical level. Critical reviews by experts cover topics ranging from astrophysics (anisotropies in the cosmic microwave background, gamma ray bursts, neutron stars and astroparticles), cosmology, the status of gravitational wave sources and detectors, verification of Newton's law at short distances, the equivalence principle, gravito-magnetism, measurement theory, time machines and the foundations of Einstein's theory, to string theory and loop quantum gravity.

Formulations of General Relativity

Author: Kirill Krasnov

Publisher: Cambridge University Press

Published: 2020-11-26

Total Pages: 391

ISBN-13: 1108481647

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Carefully documenting the different formulations of general relativity, the author reveals valuable insight into the nature of the gravitational force and its interaction with matter. This book will interest graduate students and researchers in the fields of general relativity, gravitational physics and differential geometry.

Book Synopsis Formulations of General Relativity by : Kirill Krasnov

Download or read book Formulations of General Relativity written by Kirill Krasnov and published by Cambridge University Press. This book was released on 2020-11-26 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Carefully documenting the different formulations of general relativity, the author reveals valuable insight into the nature of the gravitational force and its interaction with matter. This book will interest graduate students and researchers in the fields of general relativity, gravitational physics and differential geometry.

Noether Symmetries in Theories of Gravity

Author: Francesco Bajardi

Publisher: Cambridge University Press

Published: 2022-11-24

Total Pages: 452

ISBN-13: 100920873X

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This volume summarizes the many alternatives and extensions to Einstein's General Theory of Relativity, and shows how symmetry principles can be applied to identify physically viable models. The first part of the book establishes the foundations of classical field theory, providing an introduction to symmetry groups and the Noether theorems. A quick overview of general relativity is provided, including discussion of its successes and shortcomings, then several theories of gravity are presented and their main features are summarized. In the second part, the 'Noether Symmetry Approach' is applied to theories of gravity to identify those which contain symmetries. In the third part of the book these selected models are tested through comparison with the latest experiments and observations. This constrains the free parameters in the selected models to fit the current data, demonstrating a useful approach that will allow researchers to construct and constrain modified gravity models for further applications.

Book Synopsis Noether Symmetries in Theories of Gravity by : Francesco Bajardi

Download or read book Noether Symmetries in Theories of Gravity written by Francesco Bajardi and published by Cambridge University Press. This book was released on 2022-11-24 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume summarizes the many alternatives and extensions to Einstein's General Theory of Relativity, and shows how symmetry principles can be applied to identify physically viable models. The first part of the book establishes the foundations of classical field theory, providing an introduction to symmetry groups and the Noether theorems. A quick overview of general relativity is provided, including discussion of its successes and shortcomings, then several theories of gravity are presented and their main features are summarized. In the second part, the 'Noether Symmetry Approach' is applied to theories of gravity to identify those which contain symmetries. In the third part of the book these selected models are tested through comparison with the latest experiments and observations. This constrains the free parameters in the selected models to fit the current data, demonstrating a useful approach that will allow researchers to construct and constrain modified gravity models for further applications.

The Large Scale Structure of Space-Time

Author: Stephen W. Hawking

Publisher: Cambridge University Press

Published: 2023-02-16

Total Pages: 414

ISBN-13: 1009253182

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First published in 1973, this influential work discusses Einstein's General Theory of Relativity to show how two of its predictions arise: first, that the ultimate fate of many massive stars is to undergo gravitational collapse to form 'black holes'; and second, that there was a singularity in the past at the beginning of the universe. Starting with a precise formulation of the theory, including the necessary differential geometry, the authors discuss the significance of space-time curvature and examine the properties of a number of exact solutions of Einstein's field equations. They develop the theory of the causal structure of a general space-time, and use it to prove a number of theorems establishing the inevitability of singularities under certain conditions. A Foreword contributed by Abhay Ashtekar and a new Preface from George Ellis help put the volume into context of the developments in the field over the past fifty years.

Book Synopsis The Large Scale Structure of Space-Time by : Stephen W. Hawking

Download or read book The Large Scale Structure of Space-Time written by Stephen W. Hawking and published by Cambridge University Press. This book was released on 2023-02-16 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1973, this influential work discusses Einstein's General Theory of Relativity to show how two of its predictions arise: first, that the ultimate fate of many massive stars is to undergo gravitational collapse to form 'black holes'; and second, that there was a singularity in the past at the beginning of the universe. Starting with a precise formulation of the theory, including the necessary differential geometry, the authors discuss the significance of space-time curvature and examine the properties of a number of exact solutions of Einstein's field equations. They develop the theory of the causal structure of a general space-time, and use it to prove a number of theorems establishing the inevitability of singularities under certain conditions. A Foreword contributed by Abhay Ashtekar and a new Preface from George Ellis help put the volume into context of the developments in the field over the past fifty years.

Semiclassical and Stochastic Gravity

Author: Bei-Lok B. Hu

Publisher: Cambridge University Press

Published: 2020-03-05

Total Pages: 615

ISBN-13: 0521193575

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An overview of semi-classical gravity theory and stochastic gravity as theories of quantum gravity in curved space-time.

Book Synopsis Semiclassical and Stochastic Gravity by : Bei-Lok B. Hu

Download or read book Semiclassical and Stochastic Gravity written by Bei-Lok B. Hu and published by Cambridge University Press. This book was released on 2020-03-05 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of semi-classical gravity theory and stochastic gravity as theories of quantum gravity in curved space-time.

Tau Functions and their Applications

Author: John Harnad

Publisher: Cambridge University Press

Published: 2021-02-04

Total Pages: 549

ISBN-13: 1108637213

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Tau functions are a central tool in the modern theory of integrable systems. This volume provides a thorough introduction, starting from the basics and extending to recent research results. It covers a wide range of applications, including generating functions for solutions of integrable hierarchies, correlation functions in the spectral theory of random matrices and combinatorial generating functions for enumerative geometrical and topological invariants. A self-contained summary of more advanced topics needed to understand the material is provided, as are solutions and hints for the various exercises and problems that are included throughout the text to enrich the subject matter and engage the reader. Building on knowledge of standard topics in undergraduate mathematics and basic concepts and methods of classical and quantum mechanics, this monograph is ideal for graduate students and researchers who wish to become acquainted with the full range of applications of the theory of tau functions.

Book Synopsis Tau Functions and their Applications by : John Harnad

Download or read book Tau Functions and their Applications written by John Harnad and published by Cambridge University Press. This book was released on 2021-02-04 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tau functions are a central tool in the modern theory of integrable systems. This volume provides a thorough introduction, starting from the basics and extending to recent research results. It covers a wide range of applications, including generating functions for solutions of integrable hierarchies, correlation functions in the spectral theory of random matrices and combinatorial generating functions for enumerative geometrical and topological invariants. A self-contained summary of more advanced topics needed to understand the material is provided, as are solutions and hints for the various exercises and problems that are included throughout the text to enrich the subject matter and engage the reader. Building on knowledge of standard topics in undergraduate mathematics and basic concepts and methods of classical and quantum mechanics, this monograph is ideal for graduate students and researchers who wish to become acquainted with the full range of applications of the theory of tau functions.

Timeless Quantum Mechanics and the Early Universe

Author: Leonardo Chataignier

Publisher: Springer Nature

Published: 2022-04-04

Total Pages: 254

ISBN-13: 3030944484

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The book is based on the author's PhD thesis, which deals with the concept of time in quantum gravity and its relevance for the physics of the early Universe. It presents a consistent and complete new relational formulation of quantum gravity (more specifically, of quantum mechanics models with diffeomorphism invariance), which is applied to potentially observable cosmological effects. The work provides answers to the following questions: How can the dynamics of quantum states of matter and geometry be defined in a diffeomorphism-invariant way? What is the relevant space of physical states and which operators act on it? How are the quantum states related to probabilities in the absence of a preferred time? The answers can provide a further part of the route to constructing a fundamental theory of quantum gravity. The book is well-suited to graduate students as well as professional researchers in the fields of general relativity and gravitation, cosmology, and quantum foundations.

Book Synopsis Timeless Quantum Mechanics and the Early Universe by : Leonardo Chataignier

Download or read book Timeless Quantum Mechanics and the Early Universe written by Leonardo Chataignier and published by Springer Nature. This book was released on 2022-04-04 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is based on the author's PhD thesis, which deals with the concept of time in quantum gravity and its relevance for the physics of the early Universe. It presents a consistent and complete new relational formulation of quantum gravity (more specifically, of quantum mechanics models with diffeomorphism invariance), which is applied to potentially observable cosmological effects. The work provides answers to the following questions: How can the dynamics of quantum states of matter and geometry be defined in a diffeomorphism-invariant way? What is the relevant space of physical states and which operators act on it? How are the quantum states related to probabilities in the absence of a preferred time? The answers can provide a further part of the route to constructing a fundamental theory of quantum gravity. The book is well-suited to graduate students as well as professional researchers in the fields of general relativity and gravitation, cosmology, and quantum foundations.

2001, a Relativistic Spacetime Odyssey

Author: Ignazio Ciufolini

Publisher: World Scientific

Published: 2003

Total Pages: 528

ISBN-13: 9789812380890

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Book Synopsis 2001, a Relativistic Spacetime Odyssey by : Ignazio Ciufolini

Download or read book 2001, a Relativistic Spacetime Odyssey written by Ignazio Ciufolini and published by World Scientific. This book was released on 2003 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a comprehensive overview of our understanding of gravity at both the experimental and the theoretical level. Critical reviews by experts cover topics ranging from astrophysics (anisotropies in the cosmic microwave background, gamma ray bursts, neutron stars and astroparticles), cosmology, the status of gravitational wave sources and detectors, verification of Newton's law at short distances, the equivalence principle, gravito-magnetism, measurement theory, time machines and the foundations of Einstein's theory, to string theory and loop quantum gravity.

General Relativity and John Archibald Wheeler

Author: Ignazio Ciufolini

Publisher: Springer Science & Business Media

Published: 2010-06-22

Total Pages: 546

ISBN-13: 9048137357

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Observational and experimental data pertaining to gravity and cosmology are changing our view of the Universe. General relativity is a fundamental key for the understanding of these observations and its theory is undergoing a continuing enhancement of its intersection with observational and experimental data. These data include direct observations and experiments carried out in our solar system, among which there are direct gravitational wave astronomy, frame dragging and tests of gravitational theories from solar system and spacecraft observations. This book explores John Archibald Wheeler's seminal and enduring contributions in relativistic astrophysics and includes: the General Theory of Relativity and Wheeler's influence; recent developments in the confrontation of relativity with experiments; the theory describing gravitational radiation, and its detection in Earth-based and space-based interferometer detectors as well as in Earth-based bar detectors; the mathematical description of the initial value problem in relativity and applications to modeling gravitational wave sources via computational relativity; the phenomenon of frame dragging and its measurement by satellite observations. All of these areas were of direct interest to Professor John A. Wheeler and were seminally influenced by his ideas.

Book Synopsis General Relativity and John Archibald Wheeler by : Ignazio Ciufolini

Download or read book General Relativity and John Archibald Wheeler written by Ignazio Ciufolini and published by Springer Science & Business Media. This book was released on 2010-06-22 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Observational and experimental data pertaining to gravity and cosmology are changing our view of the Universe. General relativity is a fundamental key for the understanding of these observations and its theory is undergoing a continuing enhancement of its intersection with observational and experimental data. These data include direct observations and experiments carried out in our solar system, among which there are direct gravitational wave astronomy, frame dragging and tests of gravitational theories from solar system and spacecraft observations. This book explores John Archibald Wheeler's seminal and enduring contributions in relativistic astrophysics and includes: the General Theory of Relativity and Wheeler's influence; recent developments in the confrontation of relativity with experiments; the theory describing gravitational radiation, and its detection in Earth-based and space-based interferometer detectors as well as in Earth-based bar detectors; the mathematical description of the initial value problem in relativity and applications to modeling gravitational wave sources via computational relativity; the phenomenon of frame dragging and its measurement by satellite observations. All of these areas were of direct interest to Professor John A. Wheeler and were seminally influenced by his ideas.