Gauge Fields, Knots And Gravity

Gauge Fields, Knots And Gravity
Author :
Publisher : World Scientific Publishing Company
Total Pages : 481
Release :
ISBN-10 : 9789813103245
ISBN-13 : 9813103248
Rating : 4/5 (45 Downloads)

Synopsis Gauge Fields, Knots And Gravity by : John C Baez

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.

Gauge Fields, Knots, and Gravity

Gauge Fields, Knots, and Gravity
Author :
Publisher : World Scientific Publishing Company Incorporated
Total Pages : 465
Release :
ISBN-10 : 9810217293
ISBN-13 : 9789810217297
Rating : 4/5 (93 Downloads)

Synopsis Gauge Fields, Knots, and Gravity by : Associate Professor Department of Mathematics John C Baez

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.

Gauge Fields, Knots, and Gravity

Gauge Fields, Knots, and Gravity
Author :
Publisher : World Scientific Publishing Company Incorporated
Total Pages : 465
Release :
ISBN-10 : 9810220340
ISBN-13 : 9789810220341
Rating : 4/5 (40 Downloads)

Synopsis Gauge Fields, Knots, and Gravity by : John C. Baez

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.

Gauge Fields, Knots and Gravity

Gauge Fields, Knots and Gravity
Author :
Publisher :
Total Pages : 465
Release :
ISBN-10 : 7506291762
ISBN-13 : 9787506291767
Rating : 4/5 (62 Downloads)

Synopsis Gauge Fields, Knots and Gravity by : John C. Baez

Differential Geometry, Gauge Theories, and Gravity

Differential Geometry, Gauge Theories, and Gravity
Author :
Publisher : Cambridge University Press
Total Pages : 248
Release :
ISBN-10 : 0521378214
ISBN-13 : 9780521378215
Rating : 4/5 (14 Downloads)

Synopsis Differential Geometry, Gauge Theories, and Gravity by : M. Göckeler

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.

Gauge Theory and Variational Principles

Gauge Theory and Variational Principles
Author :
Publisher : Courier Corporation
Total Pages : 202
Release :
ISBN-10 : 9780486445465
ISBN-13 : 0486445461
Rating : 4/5 (65 Downloads)

Synopsis Gauge Theory and Variational Principles by : David Bleecker

This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas. Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field equation. Additional topics include free Dirac electron fields; interactions; calculus on frame bundle; and unification of gauge fields and gravitation. The text concludes with references, a selected bibliography, an index of notation, and a general index.

Loops, Knots, Gauge Theories and Quantum Gravity

Loops, Knots, Gauge Theories and Quantum Gravity
Author :
Publisher : Cambridge University Press
Total Pages : 344
Release :
ISBN-10 : 0521654750
ISBN-13 : 9780521654753
Rating : 4/5 (50 Downloads)

Synopsis Loops, Knots, Gauge Theories and Quantum Gravity by : Rodolfo Gambini

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.

Discrete Gauge Theory

Discrete Gauge Theory
Author :
Publisher : Imperial College Press
Total Pages : 218
Release :
ISBN-10 : 9781860947377
ISBN-13 : 1860947379
Rating : 4/5 (77 Downloads)

Synopsis Discrete Gauge Theory by : Robert Oeckl

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.

Gravitation and Gauge Symmetries

Gravitation and Gauge Symmetries
Author :
Publisher : CRC Press
Total Pages : 522
Release :
ISBN-10 : 9781420034264
ISBN-13 : 142003426X
Rating : 4/5 (64 Downloads)

Synopsis Gravitation and Gauge Symmetries by : M Blagojevic

In the course of the development of electromagnetic, weak and strong interactions, the concept of (internal) gauge invariance grew up and established itself as an unavoidable dynamical principle in particle physics. It is less known that the principle of equivalence, and the basic dynamical properties of the gravitational interaction can also be ex

Methods of Contemporary Gauge Theory

Methods of Contemporary Gauge Theory
Author :
Publisher : Cambridge University Press
Total Pages : 433
Release :
ISBN-10 : 9781009402057
ISBN-13 : 1009402056
Rating : 4/5 (57 Downloads)

Synopsis Methods of Contemporary Gauge Theory by : Yuri Makeenko