Gauge Fields, Knots and Gravity,9789810217297

Gauge Fields, Knots and Gravity

by ;
ISBN13: 9789810217297
ISBN10: 9810217293
Format: Hardcover
Pub. Date: 1994-09-01
Publisher(s): World Scientific Pub Co Inc
List Price: $138.02

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Summary

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.

Table of Contents

Preface vii
I Electromagnetism 1(158)
Maxwell's Equations
3(12)
Manifolds
15(8)
Vector Fields
23(16)
Differential Forms
39(30)
Rewriting Maxwell's Equations
69(34)
DeRham Theory in Electromagnetism
103(56)
Notes to Part I
153(6)
II Gauge Fields 159(204)
Symmetry
161(38)
Bundles and Connections
199(44)
Curvature and the Yang-Mills Equation
243(24)
Chern-Simons Theory
267(24)
Link Invariants from Gauge Theory
291(72)
Notes to Part II
353(10)
III Gravity 363(94)
Semi-Riemannian Geometry
365(22)
Einstein's Equation
387(10)
Lagrangians for General Relativity
397(16)
The ADM Formalism
413(24)
The New Variables
437(20)
Notes to Part III
451(6)
Index 457

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