Author : Rodolfo Gambini
Publisher : Cambridge University Press
Page : 341 pages
File Size : 49,43 MB
Release : 2023-01-31
Category : 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 : Rodolfo Gambini
Publisher : Cambridge University Press
Page : 344 pages
File Size : 34,85 MB
Release : 2000-07-03
Category : 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 : Jean-Luc Brylinski
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 48,67 MB
Release : 2009-12-30
Category : 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 : Colin Conrad Adams
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 38,57 MB
Release : 2004
Category : Mathematics
ISBN : 0821836781
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.
Author : Robert Oeckl
Publisher : Imperial College Press
Page : 218 pages
File Size : 23,64 MB
Release : 2005
Category : Science
ISBN : 1860947379
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.
Author : Carlo Rovelli
Publisher : Cambridge University Press
Page : 516 pages
File Size : 49,86 MB
Release : 2007-11-29
Category : Science
ISBN : 1139456156
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.
Author : Kunio Murasugi
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 37,11 MB
Release : 2009-12-29
Category : Mathematics
ISBN : 0817647198
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.
Author : Robin Durie
Publisher : Clinamen Press
Page : 282 pages
File Size : 38,16 MB
Release : 2000
Category : Science
ISBN :
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.
Author : Michael Francis Atiyah
Publisher : Cambridge University Press
Page : 112 pages
File Size : 49,32 MB
Release : 1990-08-23
Category : 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 : Peter S. Ozsváth
Publisher : American Mathematical Soc.
Page : 423 pages
File Size : 25,80 MB
Release : 2015-12-04
Category : Education
ISBN : 1470417375
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.
