Gauge fields, knots and gravity
著者
書誌事項
Gauge fields, knots and gravity
（Series on knots and everything, vol. 4）
World Scientific, c1994
- : [hardcover]
- : pbk
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注記
Includes index
Hardcover is different size: 24 cm
内容説明・目次
- 巻冊次
-
: [hardcover] ISBN 9789810217297
内容説明
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.
目次
- 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.
- 巻冊次
-
: pbk ISBN 9789810220341
内容説明
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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