Covariant Loop Quantum Gravity

An Elementary Introduction to Quantum Gravity and Spinfoam Theory

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Author: Carlo Rovelli,Francesca Vidotto

Publisher: Cambridge University Press

ISBN: 1107069629

Category: Science

Page: 266

View: 398

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

A First Course in Loop Quantum Gravity

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Author: Rodolfo Gambini,Jorge Pullin

Publisher: OUP Oxford

ISBN: 0191003239

Category: Science

Page: 192

View: 3184

This book provides an accessible introduction to loop quantum gravity and some of its applications, at a level suitable for undergraduate students and others with only a minimal knowledge of college level physics. In particular it is not assumed that the reader is familiar with general relativity and only minimally familiar with quantum mechanics and Hamiltonian mechanics. Most chapters end with problems that elaborate on the text, and aid learning. Applications such as loop quantum cosmology, black hole entropy and spin foams are briefly covered. The text is ideally suited for an undergraduate course in the senior year of a physics major. It can also be used to introduce undergraduates to general relativity and quantum field theory as part of a 'special topics' type of course.

Loops, Knots, Gauge Theories and Quantum Gravity

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Author: Rodolfo Gambini,Jorge Pullin

Publisher: Cambridge University Press

ISBN: 9780521654753

Category: Science

Page: 321

View: 3571

A self-contained introduction to applications of loop representations and knot theory in quantum gravity.

Quantum Gravity

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Author: Carlo Rovelli

Publisher: Cambridge University Press

ISBN: 1139456156

Category: Science

Page: N.A

View: 7461

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.

Approaches to Quantum Gravity

Toward a New Understanding of Space, Time and Matter

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Author: Daniele Oriti

Publisher: Cambridge University Press

ISBN: 0521860458

Category: Science

Page: 583

View: 5272

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.

Mathematical Theory of Quantum Fields

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Author: Huzihiro Araki

Publisher: Oxford University Press

ISBN: 0192539116

Category: Science

Page: N.A

View: 6688

This is an introduction to the mathematical foundations of quantum field theory, using operator algebraic methods and emphasizing the link between the mathematical formulations and related physical concepts. It starts with a general probabilistic description of physics, which encompasses both classical and quantum physics. The basic key physical notions are clarified at this point. It then introduces operator algebraic methods for quantum theory, and goes on to discuss the theory of special relativity, scattering theory, and sector theory in this context.

An Introduction to Twistor Theory

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Author: S. A. Huggett,K. P. Tod

Publisher: Cambridge University Press

ISBN: 9780521456890

Category: Mathematics

Page: 178

View: 2762

This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. It will be valuable also to the physicist as an introduction to some of the mathematics that has proved useful in these areas, and to the mathematician as an example of where sheaf cohomology and complex manifold theory can be used in physics.

Physics Meets Philosophy at the Planck Scale

Contemporary Theories in Quantum Gravity

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Author: Craig Callender,Nick Huggett

Publisher: Cambridge University Press

ISBN: 9780521664455

Category: Science

Page: 365

View: 7588

Was the first book to examine the exciting area of overlap between philosophy and quantum mechanics with chapters by leading experts from around the world.

Analysis, Manifolds, and Physics

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Author: Yvonne Choquet-Bruhat,Cécile DeWitt-Morette,Margaret Dillard Bleick

Publisher: Gulf Professional Publishing

ISBN: 9780444860170

Category: Mathematics

Page: 630

View: 499

This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.

Quantum Gravity

Third Edition

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Author: Claus Kiefer

Publisher: Oxford University Press

ISBN: 0199585202

Category: Mathematics

Page: 393

View: 1493

Quantum theory and Einstein's theory of relativity are at the centre of modern theoretical physics, yet, the consistent unification of both theories is still elusive. This book offers an up-to-date introduction into the attempts to construct a unified theory of "quantum gravity".

Basic Concepts of String Theory

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Author: Ralph Blumenhagen,Dieter Lüst,Stefan Theisen

Publisher: Springer Science & Business Media

ISBN: 3642294979

Category: Science

Page: 784

View: 353

The purpose of this book is to thoroughly prepare the reader for research in string theory at an intermediate level. As such it is not a compendium of results but intended as textbook in the sense that most of the material is organized in a pedagogical and self-contained fashion. Beyond the basics, a number of more advanced topics are introduced, such as conformal field theory, superstrings and string dualities - the text does not cover applications to black hole physics and cosmology, nor strings theory at finite temperatures. End-of-chapter references have been added to guide the reader wishing to pursue further studies or to start research in well-defined topics covered by this book.

Noncommutative Geometry

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 3-9, 2000

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Author: Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts

Publisher: Springer Science & Business Media

ISBN: 9783540203575

Category: Mathematics

Page: 356

View: 9380

Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Introduction to Superstrings

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Author: Michio Kaku

Publisher: Springer Science & Business Media

ISBN: 1468403192

Category: Science

Page: 568

View: 9211

We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough. Niels Bohr Superstring theory has emerged as the most promising candidate for a quan tum theory of all known interactions. Superstrings apparently solve a problem that has defied solution for the past 50 years, namely the unification of the two great fundamental physical theories of the century, quantum field theory and general relativity. Superstring theory introduces an entirely new physical picture into theoretical physics and a new mathematics that has startled even the mathematicians. Ironically, although superstring theory is supposed to provide a unified field theory of the universe, the theory itself often seems like a confused jumble offolklore, random rules of thumb, and intuition. This is because the develop ment of superstring theory has been unlike that of any other theory, such as general relativity, which began with a geometry and an action and later evolved into a quantum theory. Superstring theory, by contrast, has been evolving backward for the past 20 years. It has a bizarre history, beginning with the purely accidental discovery of the quantum theory in 1968 by G. Veneziano and M. Suzuki. Thumbing through old math books, they stumbled by chance on the Beta function, written down in the last century by mathematician Leonhard Euler.

Loop Quantum Gravity

The First 30 Years

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Author: Abhay Ashtekar,Jorge Pullin

Publisher: World Scientific Publishing Company

ISBN: 9789813209923

Category: Science

Page: 309

View: 5485

"Over the last decade, several important advances have occurred, that include the continuum and classical limit of the non-perturbative theory on the conceptual side, and concrete ideas on confronting quantum gravity with observations in cosmology. This volume takes the reader from basics to recent advances, thereby bridging an important gap. It presents a snapshot of the state-of-the-art in loop quantum gravity from the perspective of young leading researchers. The goal is two-fold: to provide a contemporary introduction to the entire field for students and post-docs and, an overview of the current status for more senior researchers. These overviews present the latest developments that are not discussed in existing books, particularly the applications to the cosmology of the early universe and quantum aspects of black holes"--

Introduction to Algebraic and Constructive Quantum Field Theory

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Author: John C. Baez,Irving E. Segal,Zhengfang Zhou

Publisher: Princeton University Press

ISBN: 1400862507

Category: Science

Page: 310

View: 7257

The authors present a rigorous treatment of the first principles of the algebraic and analytic core of quantum field theory. Their aim is to correlate modern mathematical theory with the explanation of the observed process of particle production and of particle-wave duality that heuristic quantum field theory provides. Many topics are treated here in book form for the first time, from the origins of complex structures to the quantization of tachyons and domains of dependence for quantized wave equations. This work begins with a comprehensive analysis, in a universal format, of the structure and characterization of free fields, which is illustrated by applications to specific fields. Nonlinear local functions of both free fields (or Wick products) and interacting fields are established mathematically in a way that is consistent with the basic physical constraints and practice. Among other topics discussed are functional integration, Fourier transforms in Hilbert space, and implementability of canonical transformations. The authors address readers interested in fundamental mathematical physics and who have at least the training of an entering graduate student. A series of lexicons connects the mathematical development with the underlying physical motivation or interpretation. The examples and problems illustrate the theory and relate it to the scientific literature. Originally published in 1992. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Towards the Mathematics of Quantum Field Theory

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Author: Frederic Paugam

Publisher: Springer Science & Business Media

ISBN: 3319045644

Category: Science

Page: 487

View: 1651

This ambitious and original book sets out to introduce to mathematicians (even including graduate students ) the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in use. This in turn promotes the interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, though mathematicians are the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the third part provides an introduction to quantum field theory, presents various renormalization methods, and discusses the quantization of factorization algebras.

Special Relativity

From Einstein to Strings

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Author: Patricia M. Schwarz,John H. Schwarz

Publisher: Cambridge University Press

ISBN: 1139449508

Category: Science

Page: N.A

View: 6998

This book provides a thorough introduction to Einstein's special theory of relativity, suitable for anyone with a minimum of one year's university physics with calculus. It is divided into fundamental and advanced topics. The first section starts by recalling the Pythagorean rule and its relation to the geometry of space, then covers every aspect of special relativity, including the history. The second section covers the impact of relativity in quantum theory, with an introduction to relativistic quantum mechanics and quantum field theory. It also goes over the group theory of the Lorentz group, a simple introduction to supersymmetry, and ends with cutting-edge topics such as general relativity, the standard model of elementary particles and its extensions, superstring theory, and a survey of important unsolved problems. Each chapter comes with a set of exercises. The book is accompanied by a CD-ROM illustrating, through interactive animation, classic problems in relativity involving motion.

Gauge Fields, Knots and Gravity

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Author: John Baez,Javier P Muniain

Publisher: World Scientific Publishing Company

ISBN: 9813103248

Category: Science

Page: 480

View: 3217

This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.

Effective Field Theories

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Author: Alexey A. Petrov,Andrew E. Blechman

Publisher: World Scientific

ISBN: 9814434930

Category: Science

Page: 320

View: 7875

This book is a broad-based text intended to help the growing student body interested in constructing and applying methods of effective field theory to solve problems in their research. It begins with a review of using symmetries to identify the relevant degrees of freedom in a problem, and then presents a variety of methods that can be used to construct various effective theories. A detailed discussion of canonical applications of effective field theory techniques with increasing complexity is given, including Fermi's weak interaction, heavy-quark effective theory, and soft-collinear effective theory. Applications of these techniques to study physics beyond the standard model, dark matter, and quantum and classical gravity are explored. Although most examples come from questions in high-energy physics, many of the methods can also be applied in condensed-matter settings. Appendices include various factoids from group theory and other topics that are used throughout the text, in an attempt to make the book self-contained.

Loop Quantum Gravity

A Theory of Quantum Space-time

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Author: Paul F. Kisak

Publisher: Createspace Independent Publishing Platform

ISBN: 9781539446460

Category:

Page: 288

View: 5451

Loop quantum gravity (LQG) had its origins with theories based on the quantum geometries of space-time. Theoretical physics has been working towards developing a theory of everything (TOE) for decades. The spirit of the effort appears to have a basis in fact as experimental evidence from The Large Hadron Collider and The Hubble Telescope continue to provide pieces of information that both confirm theories (Higgs Boson) and continue to raise new and confounding issues such as Dark Matter and Dark Energy. LQG is a remarkable attempt to incorporate the math of quantum mechanics and Einstein's theory of general relativity. A major focus is on developing the math of the geometric "granularity" or quantization of space. The fundamental concept behind LQG is that space is mathematically modeled as a very fine interconnected network of finite loops. These 'loops' form structures on the order of a Planck Length which is approximately 10 DEGREES DEGREES-35 meters. There are basically two variations being explored in LQG with one being canonical loop quantum gravity and a more recent variant known as covariant loop quantum gravity or 'spin-foam' theory. LQG is also being applied to the field of cosmology and is termed Loop Quantum Cosmology (LQC). This book is designed to be a reference and provide an overview of the topic and give the reader a structured knowledge to familiarize yourself with the topic at the most affordable price possible. The accuracy and knowledge is of an international viewpoint as the edited articles represent the inputs of many knowledgeable individuals and some of the most current knowledge on the topic, based on the date of publication.