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Gauge Fields, Knots and Gravity

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Introduces the mathematics needed to understand gravity. The book includes a rapid course on manifolds and differential forms, and covers: vector bundles, connections and curvature; the relation of gauge theory to the newly-discovered knot invariants; and Riemannian geometry.

Author(s): John Baez, Javier P Muniain
Series: Series on Knots and Everything 4
Publisher: World Scientific
Year: 1994

Language: English
Pages: 0
City: Singapore

I. Electromagnetism. --
1. Maxwell's Equations. --
2. Manifolds. --
3. Vector Fields. --
4. Differential Forms. --
5. Rewriting Maxwell's Equations. --
6. DeRham Theory in Electromagnetism. --
II. Gauge Fields. --
1. Symmetry. --
2. Bundles and Connections. --
3. Curvature and the Yang-Mills Equation. --
4. Chern-Simons Theory. --
5. Link Invariants from Gauge Theory. --
III. Gravity. --
1. Semi-Riemannian Geometry. --
2. Einstein's Equation. --
3. Lagrangians for General Relativity. --
4. ADM Formalism. --
5. New Variables.