Loops Knots Gauge Theories
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Author | : Rodolfo Gambini |
Publisher | : Cambridge University Press |
Total Pages | : 344 |
Release | : 2000-07-03 |
Genre | : Mathematics |
ISBN | : 9780521654753 |
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.
Author | : Rodolfo Gambini |
Publisher | : Cambridge University Press |
Total Pages | : 341 |
Release | : 2023-01-31 |
Genre | : Science |
ISBN | : 1009290193 |
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.
Author | : John C Baez |
Publisher | : World Scientific Publishing Company |
Total Pages | : 481 |
Release | : 1994-10-24 |
Genre | : Science |
ISBN | : 9813103248 |
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 | : Yuri Makeenko |
Publisher | : Cambridge University Press |
Total Pages | : 433 |
Release | : 2023-07-31 |
Genre | : Science |
ISBN | : 1009402056 |
Author | : John C. Baez |
Publisher | : |
Total Pages | : 256 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : |
Recent work by mathematicians and physicists has uncovered revelatory connections between knot theory and the problem of developing a quantum theory of gravity. This book, the proceedings of a workshop held to bring together researchers in knot theory and quantum gravity, features a number of expository and research papers that will aid significantly in closing the gap between the two disciplines. It will serve as a guide for mathematicians and physicists seeking to understand this rapidly developing area of research. The book represents a state-of-the-art study of current research and progress. The editor is the author of Gauge Fields, Knots, and Gravity (World Scientific), a graduate level text on the topic.
Author | : Michael Francis Atiyah |
Publisher | : Cambridge University Press |
Total Pages | : 112 |
Release | : 1990-08-23 |
Genre | : Mathematics |
ISBN | : 9780521395540 |
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.
Author | : Associate Professor Department of Mathematics John C Baez |
Publisher | : World Scientific Publishing Company Incorporated |
Total Pages | : 465 |
Release | : 1994 |
Genre | : Science |
ISBN | : 9789810217297 |
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 | : Jean-Luc Brylinski |
Publisher | : Springer Science & Business Media |
Total Pages | : 318 |
Release | : 2009-12-30 |
Genre | : Mathematics |
ISBN | : 0817647317 |
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.
Author | : Johannes Blümlein |
Publisher | : |
Total Pages | : 2947 |
Release | : 1998 |
Genre | : |
ISBN | : |
Author | : M. Göckeler |
Publisher | : Cambridge University Press |
Total Pages | : 248 |
Release | : 1989-07-28 |
Genre | : Mathematics |
ISBN | : 9780521378215 |
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.