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Author: Rodolfo Gambini
Publisher: Cambridge University Press
Published: 2023-01-31
Total Pages: 341
ISBN-13: 1009290193
DOWNLOAD EBOOKThis 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.
Author: Rodolfo Gambini
Publisher: Cambridge University Press
Published: 2000-07-03
Total Pages: 344
ISBN-13: 9780521654753
DOWNLOAD EBOOKNow 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.
Author: Yuri Makeenko
Publisher: Cambridge University Press
Published: 2023-07-31
Total Pages: 433
ISBN-13: 1009402056
DOWNLOAD EBOOKAuthor: Colin Conrad Adams
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 330
ISBN-13: 0821836781
DOWNLOAD EBOOKKnots 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.
Author: Jean-Luc Brylinski
Publisher: Springer Science & Business Media
Published: 2009-12-30
Total Pages: 318
ISBN-13: 0817647317
DOWNLOAD EBOOKThis 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.
Author: Robert Oeckl
Publisher: Imperial College Press
Published: 2005
Total Pages: 218
ISBN-13: 1860947379
DOWNLOAD EBOOKThis 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.
Author: Associate Professor Department of Mathematics John C Baez
Publisher: World Scientific Publishing Company Incorporated
Published: 1994
Total Pages: 465
ISBN-13: 9789810217297
DOWNLOAD EBOOKThis 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: Kunio Murasugi
Publisher: Springer Science & Business Media
Published: 2009-12-29
Total Pages: 348
ISBN-13: 0817647198
DOWNLOAD EBOOKThis 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.
Author: Michael Francis Atiyah
Publisher: Cambridge University Press
Published: 1990-08-23
Total Pages: 112
ISBN-13: 9780521395540
DOWNLOAD EBOOKThese 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.
Author: Carlo Rovelli
Publisher: Cambridge University Press
Published: 2015
Total Pages: 267
ISBN-13: 1107069629
DOWNLOAD EBOOKA comprehensible introduction to the most fascinating research in theoretical physics: advanced quantum gravity. Ideal for researchers and graduate students.
