The Quantization Of Gravity

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The Quantization of Gravity

Claus Gerhardt
The Quantization of Gravity Book PDF

Author : Claus Gerhardt
Publisher : Springer
Page : 200 pages
File Size : 46,5 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.

The Quantization of Gravity

Claus Gerhardt
The Quantization of Gravity Book PDF

Author : Claus Gerhardt
Publisher : Springer
Page : 0 pages
File Size : 42,9 Mb
Release : 2018-12-19
Category : Science
ISBN : 3030084418

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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.

The Quantization of Gravity

Claus Gerhardt
The Quantization of Gravity Book PDF

Author : Claus Gerhardt
Publisher : Unknown
Page : 200 pages
File Size : 53,5 Mb
Release : 2018
Category : Gravity
ISBN : 3319773720

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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.

The Meaning of Quantum Gravity

Horst-Heino Borzeszkowski,H.J. Treder
The Meaning of Quantum Gravity Book PDF

Author : Horst-Heino Borzeszkowski,H.J. Treder
Publisher : Springer Science & Business Media
Page : 140 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400938939

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The Meaning of Quantum Gravity by Horst-Heino Borzeszkowski,H.J. Treder Pdf

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.

Quantum Gravity in 2+1 Dimensions

Steven Carlip,Steven Jonathan Carlip
Quantum Gravity in 2 1 Dimensions Book PDF

Author : Steven Carlip,Steven Jonathan Carlip
Publisher : Cambridge University Press
Page : 296 pages
File Size : 46,8 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.

Experimental Search for Quantum Gravity

Sabine Hossenfelder
Experimental Search for Quantum Gravity Book PDF

Author : Sabine Hossenfelder
Publisher : Springer
Page : 120 pages
File Size : 51,6 Mb
Release : 2017-11-15
Category : Science
ISBN : 9783319645377

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Experimental Search for Quantum Gravity by Sabine Hossenfelder Pdf

This book summarizes recent developments in the research area of quantum gravity phenomenology. A series of short and nontechnical essays lays out the prospects of various experimental possibilities and their current status. Finding observational evidence for the quantization of space-time was long thought impossible. In the last decade however, new experimental design and technological advances have changed the research landscape and opened new perspectives on quantum gravity. Formerly dominated by purely theoretical constructions, quantum gravity now has a lively phenomenology to offer. From high precision measurements using macroscopic quantum oscillators to new analysis methods of the cosmic microwave background, no stone is being left unturned in the experimental search for quantum gravity. This book sheds new light on the connection of astroparticle physics with the quantum gravity problem. Gravitational waves and their detection are covered. It illustrates findings from the interconnection between general relativity, black holes and Planck stars. Finally, the return on investment in quantum-gravitation research is illuminated. The book is intended for graduate students and researchers entering the field.

Introduction to Quantum Effects in Gravity

Viatcheslav Mukhanov,Sergei Winitzki
Introduction to Quantum Effects in Gravity Book PDF

Author : Viatcheslav Mukhanov,Sergei Winitzki
Publisher : Cambridge University Press
Page : 298 pages
File Size : 54,8 Mb
Release : 2007-06-14
Category : Mathematics
ISBN : 0521868343

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Introduction to Quantum Effects in Gravity by Viatcheslav Mukhanov,Sergei Winitzki Pdf

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Lectures On Non-perturbative Canonical Gravity

Abhay Ashtekar
Lectures On Non perturbative Canonical Gravity Book PDF

Author : Abhay Ashtekar
Publisher : World Scientific
Page : 356 pages
File Size : 50,8 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.

Quantum Gravity

Domenico J. W. Giulini,Claus Kiefer,Claus Lämmerzahl
Quantum Gravity Book PDF

Author : Domenico J. W. Giulini,Claus Kiefer,Claus Lämmerzahl
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 54,8 Mb
Release : 2003-09-16
Category : Science
ISBN : 354040810X

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Quantum Gravity by Domenico J. W. Giulini,Claus Kiefer,Claus Lämmerzahl Pdf

The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spacetime cannot be fundamentally correct. Hence there should exist a broader theory comprising both in appropriate limits, i.e., quantum gravity. This book gives readers a comprehensive introduction accessible to interested non-experts to the main issues surrounding the search for quantum gravity. These issues relate to fundamental questions concerning the various formalisms of quantization; specific questions concerning concrete processes, like gravitational collapse or black-hole evaporation; and the all important question concerning the possibility of experimental tests of quantum-gravity effects.

Three Roads To Quantum Gravity

Lee Smolin
Three Roads To Quantum Gravity Book PDF

Author : Lee Smolin
Publisher : Basic Books
Page : 230 pages
File Size : 47,9 Mb
Release : 2008-03-18
Category : Science
ISBN : 9780465013241

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Three Roads To Quantum Gravity by Lee Smolin Pdf

"It would be hard to imagine a better guide to this difficult subject." -- Scientific American In Three Roads to Quantum Gravity, Lee Smolin provides an accessible overview of the attempts to build a final "theory of everything." He explains in simple terms what scientists are talking about when they say the world is made from exotic entities such as loops, strings, and black holes and tells the fascinating stories behind these discoveries: the rivalries, epiphanies, and intrigues he witnessed firsthand. "Provocative, original, and unsettling." -- The New York Review of Books "An excellent writer, a creative thinker." -- Nature

Quantum Gravity

Claus Kiefer
Quantum Gravity Book PDF

Author : Claus Kiefer
Publisher : OUP Oxford
Page : 408 pages
File Size : 41,8 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.

Relativity, Astrophysics and Cosmology

W. Israel
Relativity Astrophysics and Cosmology Book PDF

Author : W. Israel
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401026390

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Relativity, Astrophysics and Cosmology by W. Israel Pdf

The 1972 Banff lectures attempted a systematic exposition of the ideas underlying recent developments in general relativity and its astronomical applications at a level accessible and useful to graduate students having some previous acquaintance with the subject. To our regret, it was not possible to include any printed record of Peebles' beautiful lectures on observational cosmology or of the many stimulating seminars on special topics contributed by the participants. What remains is nevertheless a reason ably self-contained and compact introduction to Einstein's theory in its modern in carnation, and we hope it will be found useful by the many physicists, astronomers, and mathematicians who wish to update and deepen their understanding of the theory. On behalf of the organizing committee, I should like to express appreciation to a number of people whose help was crucial to the success of the enterprise: to Jan van Kranendonk, who initiated the idea of a Banff summer school on general relativity; to him and to David Rowe and Don Betts for inspiration and moral support; to our indefatigable secretaries Olwyn Buckland and Leslie Hughes; and to Garry Nash, Richard Sigal, Tim Spanos, and Gordon Wilson who helped in a variety of ways to keep the wheels running. How much we owe to the splendid cooperative effort of the lecturers will be clear to any reader of the following pages.

Covariant Loop Quantum Gravity

Carlo Rovelli,Francesca Vidotto
Covariant Loop Quantum Gravity Book PDF

Author : Carlo Rovelli,Francesca Vidotto
Publisher : Cambridge University Press
Page : 267 pages
File Size : 41,7 Mb
Release : 2015
Category : Science
ISBN : 9781107069626

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Covariant Loop Quantum Gravity by Carlo Rovelli,Francesca Vidotto Pdf

A comprehensible introduction to the most fascinating research in theoretical physics: advanced quantum gravity. Ideal for researchers and graduate students.

Canonical Gravity and Applications

Martin Bojowald
Canonical Gravity and Applications Book PDF

Author : Martin Bojowald
Publisher : Cambridge University Press
Page : 313 pages
File Size : 49,5 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.

Quantum Theory and Gravitation

A Marlow
Quantum Theory and Gravitation Book PDF

Author : A Marlow
Publisher : Elsevier
Page : 280 pages
File Size : 53,5 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323157971

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Quantum Theory and Gravitation by A Marlow Pdf

Quantum Theory and Gravitation provides information pertinent to quantum theory and general relativity. This book defines the problem areas and presents specific solutions to problems in relativity or quantum theory. Organized into 17 chapters, this book starts with an overview of the concept of pregeometry wherein the geometry of space and space time are based. This text then explores the restriction to real amplitude in photon polarization experiment, which appears in the fact that the elliptical polarizations are not included as possibilities. Other chapters consider the primary role that space-time models play in the expression of physical theories. This book discusses as well the basic structure of an axiomatic model for a fully relativistic quantum theory, which consists of four axioms imposed on an operational quantum logical universe of discourse. The final chapter describes the relationships between certain areas of mathematics and the developments in theoretical physics. Physicists, mathematicians, and researchers will find this book useful.