Canonical Gravity and Applications

Canonical Gravity and Applications
Author: Martin Bojowald
Publisher: Cambridge University Press
Total Pages: 313
Release: 2010-12-23
Genre: Science
ISBN: 1139494139

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.

Lectures on Non-perturbative Canonical Gravity

Lectures on Non-perturbative Canonical Gravity
Author: Abhay Ashtekar
Publisher: World Scientific
Total Pages: 356
Release: 1991
Genre: Science
ISBN: 9810205740

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.

Modern Canonical Quantum General Relativity

Modern Canonical Quantum General Relativity
Author: Thomas Thiemann
Publisher: Cambridge University Press
Total Pages: 739
Release: 2008-11-13
Genre: Science
ISBN: 113946759X

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.

Canonical Quantum Gravity

Canonical Quantum Gravity
Author: Francesco Cianfrani
Publisher: World Scientific Publishing Company Incorporated
Total Pages: 300
Release: 2014
Genre: Science
ISBN: 9789814556644

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.

Quantum Gravity in 2+1 Dimensions

Quantum Gravity in 2+1 Dimensions
Author: Steven Carlip
Publisher: Cambridge University Press
Total Pages: 296
Release: 2003-12-04
Genre: Science
ISBN: 9780521545884

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

Classical and Quantum Cosmology

Classical and Quantum Cosmology
Author: Gianluca Calcagni
Publisher: Springer
Total Pages: 854
Release: 2017-01-06
Genre: Science
ISBN: 3319411276

This comprehensive textbook is devoted to classical and quantum cosmology, with particular emphasis on modern approaches to quantum gravity and string theory and on their observational imprint. It covers major challenges in theoretical physics such as the big bang and the cosmological constant problem. An extensive review of standard cosmology, the cosmic microwave background, inflation and dark energy sets the scene for the phenomenological application of all the main quantum-gravity and string-theory models of cosmology. Born of the author's teaching experience and commitment to bridging the gap between cosmologists and theoreticians working beyond the established laws of particle physics and general relativity, this is a unique text where quantum-gravity approaches and string theory are treated on an equal footing. As well as introducing cosmology to undergraduate and graduate students with its pedagogical presentation and the help of 45 solved exercises, this book, which includes an ambitious bibliography of about 3500 items, will serve as a valuable reference for lecturers and researchers.

Relativity, Astrophysics and Cosmology

Relativity, Astrophysics and Cosmology
Author: W. Israel
Publisher: Springer Science & Business Media
Total Pages: 342
Release: 2012-12-06
Genre: Science
ISBN: 9401026394

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.

The Quantization of Gravity

The Quantization of Gravity
Author: Claus Gerhardt
Publisher: Springer
Total Pages: 0
Release: 2024-10-09
Genre: Science
ISBN: 9783031679216

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.

Fundamental Interactions

Fundamental Interactions
Author: Daniel Grumiller
Publisher: World Scientific
Total Pages: 422
Release: 2010
Genre: Science
ISBN: 9814277835

This memorial volume on the work of Wolfgang Kummer brings together articles devoted to the history of high energy physics with detailed coverage on the scientific concepts and scientific institutions, in particular CERN OCo and the underlying physics involved. Covering recent advances and developments as well as giving a reminiscent overview in two rapidly evolving fields of high energy/particle physics, and gravitational physics, the commemorative volume contains more than 20 original invited paper contributions OCo which will appear for the first time in print OCo from eminent and renowned physicists who interacted and collaborated with Wolfgang Kummer, including Physics Nobel Laureate Jack Steinberger. Wolfgang Kummer was president of the CERN council from 1985 to 1987, among his numerous eminent academic and administrative positions which he held during his illustrious career. This volume also aims to demonstrate and highlight Wolfgang Kummer''s significant contribution to the foundational work in gauge field theory, particle physics, and quantum gravity, and the tremendous impact leading to cutting-edge findings and advances at LHC. Sample Chapter(s). Foreword (155 KB). Chapter 1: Noncovariant Gauges at Zero and Nonzero Temperature (215 KB). Contents: Gauge Field Theory and Particle Physics: Noncovariant Gauges at Zero and Nonzero Temperature (P V Landshoff); Non-Relativistic Bound States: The Long Way Back from the BetheOCoSalpeter to the SchrAdinger Equation (A Vairo); Distended/Diminished Topologically Massive Electrodynamics (S Deser); Dynamical Spin (P G O Freund); Quantum Corrections to Solitons and BPS Saturation (A Rebhan et al.); Gauging Noncommutative Theories (H Grosse & M Wohlgenannt); Topological Phases and Contextuality Effects in Neutron Quantum Optics (H Rauch); First Class Constrained Systems and Twisting of Courant Algebroids by a Closed 4-Form (M Hansen & T Strobl); Some Local and Global Aspects of the Gauge Fixing in YangOCoMills-Theories (D N Blaschke et al.); Frozen Ghosts in Thermal Gauge Field Theory (P V Landshoff & A Rebhan); Classical and Quantum Gravity: Wolfgang Kummer and the Vienna School of Dilaton (Super-)Gravity (L Bergamin & R Meyer); Order and Chaos in Two Dimensional Gravity (R B Mann); 2-D Midisuperspace Models for Quantum Black Holes (J Gegenberg & G Kunstatter); Global Solutions in Gravity. Euclidean Signature (M O Katanaev); Thoughts on the Cosmological Principle (D J Schwarz); When Time Emerges (C Faustmann et al.); Towards Noncommutative Gravity (D V Vassilevich); Superembedding Approach to Superstring in AdS 5 X S 5 Superspace (I A Bandos); Heterotic (0,2) Gepner Models and Related Geometries (M Kreuzer); Canonical Analysis of Cosmological Topologically Massive Gravity at the Chiral Point (D Grumiller et al.); Wolfgang Kummer and the Physics Community: Wolfgang Kummer at CERN (H Schopper); Wolfgang Kummer and the Little Lost Lane Boy (K Lane); Mitigation of Fossil Fuel Consumption and Global Warming by Thermal Solar Electric Power Production in the World''s Deserts (J Steinberger); (My) Life with Wolfgang Kummer (M Schweda); Schubert in Stony Brook and Kinks in Vienna (P van Nieuwenhuizen). Readership: Scientists, researchers, graduates and undergraduates interested in high energy, particle or gravitational physics."