This work shows how the concepts of manifold theory can be used to describe the physical world. The concepts of modern differential geometry are presented in this comprehensive study of classical mechanics, field theory, and simple quantum effects.
| Introduction. Classical Mechanics. Introduction to Differential Manifolds. Differential Equations on Manifolds. The Tangent and Cotangent Bundles. Covariant 2-Tensors and Metric Structures. Lagrangian and Hamiltonian Mechanics for Holonomic Systems. Tensors. Differential Forms. Integration of Differential Forms. The Special Theory of Relativity. Electromagnetic Theory. The Mechanics of Rigid Body Motion. Lie Groups. Geometrical Models. Principal Bundles and Connections |
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| Gauge Fields and Classical Particles. Quantum Effects, Line Bundles, and Holonomy Groups. Physical Laws for the Gauge Fields. Bibliography. Index. |
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