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Classical And Quantum Gravity

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From Classical To Quantum Mechanics

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Author : Giampiero Esposito
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-11

From Classical To Quantum Mechanics written by Giampiero Esposito 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 2004-03-11 with Science categories.

This 2004 textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material which is necessary to understand the transition from classical to wave mechanics. Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton-Jacobi equation, the Cauchy problem for the wave equation, Helmholtz equation and eikonal approximation, introduction to spin, perturbation theory and scattering theory. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. Part III is devoted to topics such as statistical mechanics and black-body radiation, Lagrangian and phase-space formulations of quantum mechanics, and the Dirac equation. This book is intended for use as a textbook for beginning graduate and advanced undergraduate courses. It is self-contained and includes problems to aid the reader's understanding.

Quantum Gravity Quantum Cosmology And Lorentzian Geometries

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Author : Giampiero Esposito
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-01-28

Quantum Gravity Quantum Cosmology And Lorentzian Geometries written by Giampiero Esposito and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-28 with Computers categories.

The first aim of this book is to describe recent work on the problem of boundary conditions in one-loop quantum cosmology. The motivation is to understand whether supersymmetric theories are one-loop finite in the presence of boundaries. The second aim of the book is to present a recent, entirely new study of the singularity problem for space-times with torsion. The book is written in self-contained form. In many cases problems have been initially formulated in the simplest possible way, and finally presented and solved at increasing levels of complexity. Readers will find here a detailed and updated study of quantum cosmology, its motivation, and application to perturbative quantum gravity. Moreover, this is the first book which enables the reader to learn techniques used in classical gravity and quantum cosmology. The second edition adds new material to both the text and the bibliography.

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.

Quantum Gravity

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Author : Carlo Rovelli
language : en
Publisher: Cambridge University Press
Release Date : 2007-11-29

Quantum Gravity written by Carlo Rovelli 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 2007-11-29 with Science categories.

Quantum gravity is perhaps the most important open problem in fundamental physics. It is the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this 2004 book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

Finite Mathematics As The Foundation Of Classical Mathematics And Quantum Theory

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Author : Felix Lev
language : en
Publisher: Springer Nature
Release Date : 2020-11-03

Finite Mathematics As The Foundation Of Classical Mathematics And Quantum Theory written by Felix Lev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-03 with Science categories.

This book delves into finite mathematics and its application in physics, particularly quantum theory. It is shown that quantum theory based on finite mathematics is more general than standard quantum theory, whilst finite mathematics is itself more general than standard mathematics.As a consequence, the mathematics describing nature at the most fundamental level involves only a finite number of numbers while the notions of limit, infinite/infinitesimal and continuity are needed only in calculations that describe nature approximately. It is also shown that the concepts of particle and antiparticle are likewise approximate notions, valid only in special situations, and that the electric charge and baryon- and lepton quantum numbers can be only approximately conserved.

Semiclassical And Stochastic Gravity

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Author : Bei-Lok B. Hu
language : en
Publisher: Cambridge University Press
Release Date : 2020-03-05

Semiclassical And Stochastic Gravity written by Bei-Lok B. Hu 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 2020-03-05 with Science categories.

The two pillars of modern physics are general relativity and quantum field theory, the former describes the large scale structure and dynamics of space-time, the latter, the microscopic constituents of matter. Combining the two yields quantum field theory in curved space-time, which is needed to understand quantum field processes in the early universe and black holes, such as the well-known Hawking effect. This book examines the effects of quantum field processes back-reacting on the background space-time which become important near the Planck time (10-43 sec). It explores the self-consistent description of both space-time and matter via the semiclassical Einstein equation of semiclassical gravity theory, exemplified by the inflationary cosmology, and fluctuations of quantum fields which underpin stochastic gravity, necessary for the description of metric fluctuations (space-time foams). Covering over four decades of thematic development, this book is a valuable resource for researchers interested in quantum field theory, gravitation and cosmology.

Foundations Of Quantum Cosmology

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Author : Martin Bojowald
language : en
Publisher:
Release Date : 2020-09-25

Foundations Of Quantum Cosmology written by Martin Bojowald and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-25 with categories.

This is the first book to lay the physical foundations of quantum cosmology, complete with an introduction to space-time physics, quantum theory, and the main approaches to quantum gravity. It is an essential guide for researchers in quantum gravity and astrophysicists interested in fundamental aspects of cosmology.

Approaches To Quantum Gravity

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Author : Daniele Oriti
language : en
Publisher: Cambridge University Press
Release Date : 2009-03-05

Approaches To Quantum Gravity written by Daniele Oriti 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 2009-03-05 with Science categories.

Containing contributions from leading researchers in this field, this book provides a complete overview of this field from the frontiers of theoretical physics research for graduate students and researchers. It introduces the most current approaches to this problem, and reviews their main achievements.