The Quantization Of Gravity
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The Quantization Of Gravity
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Author : Claus Gerhardt
language : en
Publisher: Springer
Release Date : 2024-10-09
The Quantization Of Gravity written by Claus Gerhardt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-09 with Science categories.
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 hyperbolic equation in a fiber bundle, where the base space represents a Cauchy hypersurface of the quantized spacetime and the fibers the Riemannian metrics in the base space. The hyperbolic operator, a second order partial differential operator, acts both in the fibers as well as in the base space. In this second edition new results are presented which allow the solutions of the hyperbolic equation to be expressed as products of spatial and temporal eigenfunctions of self-adjoint operators. These eigenfunctions form complete bases in appropriate Hilbert spaces. The eigenfunctions depending on the fiber elements are a subset of the Fourier kernel of the symmetric space SL(n,R)/SO(n), where n is the dimension of the base space; they represent the elementary gravitons corresponding to the degrees of freedom in choosing the entries of Riemannian metrics with determinants equal to one. These are all the degrees of freedom available because of the coordinate system invariance: For any smooth Riemannian metric there exists an atlas such that in each chart the determinant of the metric is equal to one. In the important case n=3 the Standard Model could also be incorporated such that one can speak of a unified quantization of all four fundamental forces of nature.
The Quantization Of Gravity
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Author : Claus Gerhardt
language : en
Publisher: Springer Nature
Release Date : 2024-11-05
The Quantization Of Gravity written by Claus Gerhardt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Science categories.
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 hyperbolic equation in a fiber bundle, where the base space represents a Cauchy hypersurface of the quantized spacetime and the fibers the Riemannian metrics in the base space. The hyperbolic operator, a second order partial differential operator, acts both in the fibers as well as in the base space. In this second edition new results are presented which allow the solutions of the hyperbolic equation to be expressed as products of spatial and temporal eigenfunctions of self-adjoint operators. These eigenfunctions form complete bases in appropriate Hilbert spaces. The eigenfunctions depending on the fiber elements are a subset of the Fourier kernel of the symmetric space SL(n,R)/SO(n), where n is the dimension of the base space; they represent the elementary gravitons corresponding to the degrees of freedom in choosing the entries of Riemannian metrics with determinants equal to one. These are all the degrees of freedom available because of the coordinate system invariance: For any smooth Riemannian metric there exists an atlas such that in each chart the determinant of the metric is equal to one. In the important case n=3 the Standard Model could also be incorporated such that one can speak of a unified quantization of all four fundamental forces of nature.
Quantum Gravity In 2 1 Dimensions
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Author : Steven Carlip
language : en
Publisher: Cambridge University Press
Release Date : 2003-12-04
Quantum Gravity In 2 1 Dimensions written by Steven Carlip and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-04 with Science categories.
The first comprehensive survey of (2+1)-dimensional quantum gravity - for graduate students and researchers.
Introduction To Quantum Effects In Gravity
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Author : Viatcheslav Mukhanov
language : en
Publisher: Cambridge University Press
Release Date : 2007-06-14
Introduction To Quantum Effects In Gravity written by Viatcheslav Mukhanov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-14 with Mathematics categories.
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Conversations On Quantum Gravity
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Author : Jácome Armas
language : en
Publisher: Cambridge University Press
Release Date : 2021-08-26
Conversations On Quantum Gravity written by Jácome Armas and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-26 with Biography & Autobiography categories.
Leading theorists share their important insights into the ongoing quest of theoretical physics to find a quantum theory of gravity.
Foundations Of Space And Time
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Author : Jeff Murugan
language : en
Publisher: Cambridge University Press
Release Date : 2012-07-19
Foundations Of Space And Time written by Jeff Murugan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-19 with Science categories.
Encapsulates the latest debates on this topic, giving researchers and graduate students an up-to-date view of the field.
Quantum Field Theory Ii
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Author : Edouard B. Manoukian
language : en
Publisher: Springer
Release Date : 2016-09-26
Quantum Field Theory Ii written by Edouard B. Manoukian and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-26 with Science categories.
This book takes a pedagogical approach to explaining quantum gravity, supersymmetry and string theory in a coherent way. It is aimed at graduate students and researchers in quantum field theory and high-energy physics. The first part of the book introduces quantum gravity, without requiring previous knowledge of general relativity (GR). The necessary geometrical aspects are derived afresh leading to explicit general Lagrangians for gravity, including that of general relativity. The quantum aspect of gravitation, as described by the graviton, is introduced and perturbative quantum GR is discussed. The Schwinger-DeWitt formalism is developed to compute the one-loop contribution to the theory and renormalizability aspects of the perturbative theory are also discussed. This follows by introducing only the very basics of a non-perturbative, background-independent, formulation of quantum gravity, referred to as “loop quantum gravity”, which gives rise to a quantization of space. In the second part the author introduces supersymmetry and its consequences. The generation of superfields is represented in detail. Supersymmetric generalizations of Maxwell’s Theory as well as of Yang-Mills field theory, and of the standard model are worked out. Spontaneous symmetry breaking, improvement of the divergence problem in supersymmetric field theory, and its role in the hierarchy problem are covered. The unification of the fundamental constants in a supersymmetric version of the standard model are then studied. Geometrical aspects necessary to study supergravity are developed culminating in the derivation of its full action. The third part introduces string theory and the analysis of the spectra of the mass (squared) operator associated with the oscillating strings. The properties of the underlying fields, associated with massless particles, encountered in string theory are studied in some detail. Elements of compactification, duality and D-branes are given, as well of the generation of vertices and interactions of strings. In the final sections, the author shows how to recover GR and the Yang-Mills field Theory from string theory.
Lectures On Non Perturbative Canonical Gravity
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Author : Abhay Ashtekar
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 1991
Lectures On Non Perturbative Canonical Gravity written by Abhay Ashtekar and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Science categories.
Pt. I. Introduction. 1. Non-perturbative quantum gravity: what and why? -- 2. Overview -- pt. II. Classical theory. 3. Lagrangian framework -- 4. Legendre transform: details -- 5. From triads to SU(2) spinors: a quick transition -- 6. Hamiltonian formulation -- 7. Constraint algebra, Hamiltonians and dynamics -- 8. Reality conditions -- 9. Inclusion of matterpart -- pt. III. Quantum theory. 10. The quantization program -- 11. Connection representation: linearized gravity -- 12. Connection representation: issue of time -- 13. Connection representation: CP problem -- 14. Loop representation: Maxwell theory -- 15. Loop representation: classical theory -- 16. Loop representation: quantum theory -- 17. 2 + 1 gravity
The Problem Of Time
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Author : Edward Anderson
language : en
Publisher: Springer
Release Date : 2017-09-18
The Problem Of Time written by Edward Anderson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-18 with Science categories.
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.
Fields Of Color
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Author : Rodney A Brooks
language : en
Publisher: Independently Published
Release Date : 2010-12-14
Fields Of Color written by Rodney A Brooks and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-14 with categories.
Fields of Color explains Quantum Field Theory to a lay audience without equations. It shows how this often overlooked theory resolves the weirdness of Quantum Mechanics and the paradoxes of Relativity. The third edition contains a new solution to the measurement problem ("the most controversial problem in physics today") and shows the quantum basis for Einstein's famous E = mc2.