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 Contents0. 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
8. Calculus on Frame Bundle
9. Unification of Gauge Fields and Gravitation
10. Additional Topics
Index of Notation