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Gauge Theory and Variational Principles
by David Bleecker
This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas.
Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field equation. Additional topics include free Dirac electron fields; interactions; calculus on frame bundle; and unification of gauge fields and gravitation. The text concludes with references, a selected bibliography, an index of notation, and a general index.
Table of Contents for Gauge Theory and Variational Principles
| 0. Preliminaries | | 1. Principal Fiber Bundles and Connections | | 2. Curvature and G-Valued Differential Forms | | 3. Particle Fields, Lagrangians, Gauge Invariance | | 4. Lagrange’s Equation for Particle Fields | | 5. The Inhomogeneous Field Equation | | 6. Free Dirac Electron Fields | | 7. Interactions | | 8. Calculus on Frame Bundle | | 9. Unification of Gauge Fields and Gravitation | | 10. Additional Topics | | References | | Selected Bibliography | | Index of Notation | | Index |
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