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
|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|
|8. Calculus on Frame Bundle|
|9. Unification of Gauge Fields and Gravitation|
|10. Additional Topics|
|Index of Notation|