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Gauge Fields, Knots and Gravity : World Scientific Series on Nonlinear Science - John Baez

Gauge Fields, Knots and Gravity

World Scientific Series on Nonlinear Science

Hardcover

Published: January 1994
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  • Paperback View Product Published: 24th October 1994
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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.

"This book is a great introduction to many of the modern ideas of mathematical physics including differential geometry, group theory, knot theory and topology. It uses as 'physical excuses' to introduce these topics Maxwell theory, Yang-Mills theories and general relativity (including its Ashtekar reformulation). The level of the book is gauged to advanced physics/math undergraduates and graduate students. The style of the book is quite lively and explanations are very clear. The treatment is mathematically and physically self-contained ... I would strongly recommend this nicely written book for anyone interested in teaching the contemporary ideas of mathematical physics to an audience of physicists (especially if that audience is interested in particle physics/gravity). It offers an excellent way of treating the subject with mathematical rigor while keeping the physical motivation and usefulness of these mathematical concepts close at hand. For the individual reader, it is a great way to be lured into the study of the mathematics that underlies contemporary theoretical physics."

Preface
Electromagnetismp. 1
Maxwell's Equationsp. 3
Manifoldsp. 15
Vector Fieldsp. 23
Differential Formsp. 39
Rewriting Maxwell's Equationsp. 69
DeRham Theory in Electromagnetismp. 103
Gauge Fieldsp. 159
Symmetryp. 161
Bundles and Connectionsp. 199
Curvature and the Yang-Mills Equationp. 243
Chern-Simons Theoryp. 267
Link Invariants from Gauge Theoryp. 291
Gravityp. 363
Semi-Riemannian Geometryp. 365
Einstein's Equationp. 387
Lagrangians for General Relativityp. 397
The ADM Formalismp. 413
The New Variablesp. 437
Indexp. 457
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9789810217297
ISBN-10: 9810217293
Series: World Scientific Series on Nonlinear Science
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 480
Published: January 1994
Country of Publication: SG
Dimensions (cm): 21.84 x 15.75  x 3.05
Weight (kg): 0.79