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Loops Knots Gauge Theories
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Book Synopsis Loops, Knots, Gauge Theories and Quantum Gravity by : Rodolfo Gambini
Download or read book Loops, Knots, Gauge Theories and Quantum Gravity written by Rodolfo Gambini and published by Cambridge University Press. This book was released on 2000-07-03 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in paperback, this text provides a self-contained introduction to applications of loop representations and knot theory in particle physics and quantum gravity. Loop representations (and the related topic of knot theory) are of considerable current interest because they provide a unified arena for the study of the gauge invariant quantization of Yang-Mills theories and gravity, and suggest a promising approach to the eventual unification of the four fundamental forces. This text begins with a detailed review of loop representation theory. It then goes on to describe loop representations in Maxwell theory, Yang-Mills theories as well as lattice techniques. Applications in quantum gravity are then discussed in detail. Following chapters move on to consider knot theories, braid theories and extended loop representations in quantum gravity. A final chapter assesses the current status of the theory and points out possible directions for future research.
Book Synopsis Loops, Knots, Gauge Theories by : Rodolfo Gambini
Download or read book Loops, Knots, Gauge Theories written by Rodolfo Gambini and published by Cambridge University Press. This book was released on 2023-01-31 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a self-contained introduction to applications of loop representations in particle physics and quantum gravity, in order to explore the gauge invariant quantization of Yang-Mills theories and gravity. First published in 1996, this title has been reissued as an Open Access publication on Cambridge Core.
Book Synopsis Methods of Contemporary Gauge Theory by : Yuri Makeenko
Download or read book Methods of Contemporary Gauge Theory written by Yuri Makeenko and published by Cambridge University Press. This book was released on 2023-07-31 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Loop Spaces, Characteristic Classes and Geometric Quantization by : Jean-Luc Brylinski
Download or read book Loop Spaces, Characteristic Classes and Geometric Quantization written by Jean-Luc Brylinski and published by Springer Science & Business Media. This book was released on 2009-12-30 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge.
Book Synopsis Gauge Fields, Knots and Gravity by : John Baez
Download or read book Gauge Fields, Knots and Gravity written by John Baez and published by World Scientific Publishing Company. This book was released on 1994-10-24 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :Clay Mathematics Institute. Summer School Publisher :American Mathematical Soc. ISBN 13 :9780821838457 Total Pages :318 pages Book Rating :4.8/5 (384 download)
Book Synopsis Floer Homology, Gauge Theory, and Low-Dimensional Topology by : Clay Mathematics Institute. Summer School
Download or read book Floer Homology, Gauge Theory, and Low-Dimensional Topology written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2006 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electro-weak and strong nuclear forces. The use of gauge theory as a tool for studying topological properties of four-manifolds was pioneered by the fundamental work of Simon Donaldson in theearly 1980s, and was revolutionized by the introduction of the Seiberg-Witten equations in the mid-1990s. Since the birth of the subject, it has retained its close connection with symplectic topology. The analogy between these two fields of study was further underscored by Andreas Floer's constructionof an infinite-dimensional variant of Morse theory that applies in two a priori different contexts: either to define symplectic invariants for pairs of Lagrangian submanifolds of a symplectic manifold, or to define topological This volume is based on lecture courses and advanced seminars given at the 2004 Clay Mathematics Institute Summer School at the Alfred Renyi Institute of Mathematics in Budapest, Hungary. Several of the authors have added a considerable amount of additional material tothat presented at the school, and the resulting volume provides a state-of-the-art introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds. Information for our distributors: Titles in this seriesare copublished with the Clay Mathematics Institute (Cambridge, MA).
Book Synopsis Differential Geometry, Gauge Theories, and Gravity by : M. Göckeler
Download or read book Differential Geometry, Gauge Theories, and Gravity written by M. Göckeler and published by Cambridge University Press. This book was released on 1989-07-28 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.
Book Synopsis The Knot Book by : Colin Conrad Adams
Download or read book The Knot Book written by Colin Conrad Adams and published by American Mathematical Soc.. This book was released on 2004 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.
Book Synopsis Discrete Gauge Theory by : Robert Oeckl
Download or read book Discrete Gauge Theory written by Robert Oeckl and published by Imperial College Press. This book was released on 2005 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to topological quantum field theory as well as discrete gauge theory with quantum groups. In contrast to much of the existing literature, the present approach is at the same time intuitive and mathematically rigorous, making extensive use of suitable diagrammatic methods. It provides a highly unified description of lattice gauge theory, topological quantum field theory and models of quantum (super)gravity. The reader is thus in a unique position to understand the relations between these subjects as well as the underlying groundwork.
Book Synopsis A First Course in Loop Quantum Gravity by : Rodolfo Gambini
Download or read book A First Course in Loop Quantum Gravity written by Rodolfo Gambini and published by OUP Oxford. This book was released on 2011-09-22 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Time & the Instant written by Robin Durie and published by Clinamen Press. This book was released on 2000 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Debating the nature of time, this collection of essays includes both the physicist's and the philosopher's viewpoint, questioning whether time exists, whether it is absolute or relative and whether it is continuous or fragmented.
Book Synopsis Grid Homology for Knots and Links by : Peter S. Ozsváth
Download or read book Grid Homology for Knots and Links written by Peter S. Ozsváth and published by American Mathematical Soc.. This book was released on 2015-12-04 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.
Book Synopsis Covariant Loop Quantum Gravity by : Carlo Rovelli
Download or read book Covariant Loop Quantum Gravity written by Carlo Rovelli and published by Cambridge University Press. This book was released on 2015 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensible introduction to the most fascinating research in theoretical physics: advanced quantum gravity. Ideal for researchers and graduate students.
Book Synopsis Knot Theory and Its Applications by : Kunio Murasugi
Download or read book Knot Theory and Its Applications written by Kunio Murasugi and published by Springer Science & Business Media. This book was released on 2009-12-29 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It also covers more recent developments and special topics, such as chord diagrams and covering spaces. The author avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory. Numerous diagrams and exercises help readers understand and apply the theory. Each chapter includes a supplement with interesting historical and mathematical comments.
Book Synopsis Two-loop Calculations in Gauge Theories by : Abilio De Freitas
Download or read book Two-loop Calculations in Gauge Theories written by Abilio De Freitas and published by . This book was released on 2002 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Geometry and Physics of Knots by : Michael Francis Atiyah
Download or read book The Geometry and Physics of Knots written by Michael Francis Atiyah and published by Cambridge University Press. This book was released on 1990-08-23 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes deal with an area that lies at the crossroads of mathematics and physics and rest primarily on the pioneering work of Vaughan Jones and Edward Witten, who related polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions.
Download or read book Quantum Gravity written by Carlo Rovelli and published by Cambridge University Press. This book was released on 2007-11-29 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
