| Preface Chapter 0. Preliminaries 0.1. Multilinear Algebra and Forms 0.2. Manifolds and Tensor Analysis 0.3. Lie Groups and Lie Algebras Chapter 1. Principal Fiber Bundles and Connections 1.1. Principal Fiber Bundles 1.2. Connections Chapter 2. Curvature and g-Valued Differential Forms 2.1 Graded Lie Algebra of .~-Valued Forms 2.2 Curvature Chapter 3. Particle Fields. Lagrangians. Gauge Invariance 3.1. Particle Fields 3.2. Gauge Transformations 3.3. Lagrangians and Gauge Invariance Chapter 4. Lagrange's Equation for Particle Fields 4.1. The Principle of Least Action 4.2. Some Machinery 4.3. Lagrange's Equation Chapter 5. The Inhomogeneous Field Equation 5.1. The Current 5.2. Inhomogeneous Field Equation Chapter 6. Free Dirac Electron Fields 6.1. Covering the Lorentz Group 6.2. The Levi-Cevita Connection 6.3. Spin Structures and the Lagrangian 6.4. Dirac's Equation Chapter 7. Interactions 7.1. Bundle Splicing 7.2. The (Nonfree) Dirac Electron Field 7.3. The Nucleon in a Yang-Mills Potential Chapter 8. Calculus on Frame Bundle 8.1. Tensor Fields on L(M) 8.2. Pseudo-Riemannian Geometry 8.3. Metric Variations Chapter 9. Unification of Gauge Fields and Gravitation Chapter 10. Additional Topics References Selected Bibliography Index of Notation Index Errata |
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