Gauge fields, knots and gravity
Author(s)
Bibliographic Information
Gauge fields, knots and gravity
（Series on knots and everything, vol. 4）
World Scientific, c1994
- : [hardcover]
- : pbk
Available at / 51 libraries
-
Science and Technology Library, Kyushu University
: pbk421.3/B 14031212015000843,
068222194007257 -
Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc20:530.1/b1452070317297
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Note
Includes index
Hardcover is different size: 24 cm
Description and Table of Contents
- Volume
-
: [hardcover] ISBN 9789810217297
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.
Table of Contents
- Electromagnetism: Maxwell's Equations
- Manifolds
- Vector Fields and Tangent Vectors
- Differential Forms
- Rewriting Maxwell's Equations
- De Rham Theory in Electromagnetism
- Braids, Knots and Electromagnetism
- Quantizing the Free Electromagnetic Field
- Gauge Theory.- Gauge Groups
- Connections and Parallel Transport
- Curvature and the Yang-Mills Equations
- Chern-Simons Theory
- Link Invariants from Gauge Theory. Gravity: Riemannian and Lorentzian Geometry
- Einstein's Equations
- The Lagrangian Approach to General Relativity
- The ADM Formalism
- The New Variables
- Knots and Quantum Gravity.
- Volume
-
: pbk ISBN 9789810220341
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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