Gauge Fields, Knots and Gravity

ISBN-10: 9810220340

ISBN-13: 9789810220341

Edition: N/A

Authors: J. Baez, J. Muniain

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Description:

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.
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Book details

Publisher: World Scientific Publishing Company, Incorporated
Binding: Paperback
Pages: 396
Size: 6.00" wide x 8.25" long x 1.00" tall
Weight: 1.386
Language: English

Preface
Electromagnetism
Maxwell's Equations
Manifolds
Vector Fields
Differential Forms
Rewriting Maxwell's Equations
DeRham Theory in Electromagnetism
Gauge Fields
Symmetry
Bundles and Connections
Curvature and the Yang-Mills Equation
Chern-Simons Theory
Link Invariants from Gauge Theory
Gravity
Semi-Riemannian Geometry
Einstein's Equation
Lagrangians for General Relativity
The ADM Formalism
The New Variables
Index
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