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Gauge Fields, Knots and Gravity

By: Javier P Muniain, John Baez

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Hardcover | 1 January 1994

At a Glance

Hardcover
486 Pages

Dimensions(cm)
23.6 x 16.0 x 3.3

Hardcover

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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.

Industry Reviews

"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."

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Preface
Electromagnetism	p. 1
Maxwell's Equations	p. 3
Manifolds	p. 15
Vector Fields	p. 23
Differential Forms	p. 39
Rewriting Maxwell's Equations	p. 69
DeRham Theory in Electromagnetism	p. 103
Gauge Fields	p. 159
Symmetry	p. 161
Bundles and Connections	p. 199
Curvature and the Yang-Mills Equation	p. 243
Chern-Simons Theory	p. 267
Link Invariants from Gauge Theory	p. 291
Gravity	p. 363
Semi-Riemannian Geometry	p. 365
Einstein's Equation	p. 387
Lagrangians for General Relativity	p. 397
The ADM Formalism	p. 413
The New Variables	p. 437
Index	p. 457
Table of Contents provided by Blackwell. All Rights Reserved.

Gauge Fields, Knots and Gravity

At a Glance

Hardcover

Industry Reviews

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How to return your order

Defective items

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