## Differential Manifolds and Theoretical PhysicsDifferential Manifolds and Theoretical Physics |

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### Contents

1 | |

5 | |

16 | |

Chapter 4 Differential Equations on Manifolds | 39 |

Chapter 5 The Tangent and Cotangent Bundles | 61 |

Chapter 6 Covariant 2Tensors and Metric Structures | 72 |

Chapter 7 Lagrangian and Hamiltonian Mechanics for Holonomic Systems | 94 |

Chapter 8 Tensors | 127 |

Chapter 12 Electromagnetic Theory | 239 |

Chapter 13 The Mechanics of Rigid Body Motion | 255 |

Chapter 14 Lie Groups | 286 |

Chapter 15 Geometrical Models | 297 |

Chapter 16 Principal Bundles and Connections Gauge Fields and Classical Particles | 335 |

Chapter 17 Quantum Effects Line Bundles and Holonomy Groups | 354 |

Chapter 18 Physical Laws for the Gauge Fields | 371 |

387 | |

### Common terms and phrases

action of G basis body motion canonical Chapter chart Choose components configuration space connection consider curvature form d/dt defined DEFINITION denoted diffeomorphism differential forms differential manifold differential structure equations EXAMPLE Exercise follows function G x T.G G/Go gauge geodesic given gives Hamiltonian system integral curve k-form kinetic energy Lagrangian Lemma Let f Lie algebra Lie group Lorentz frame Lorentz metric matrix momentum n-dimensional n-manifold Ö/öx obtained open set orthonormal particle phase space positively oriented principal G-bundle PRoof PROPOSITION Prove REMARK Riemannian rigid body smooth mapping smooth vector ſº space motion spacetime subbundle submanifold subspace Suppose tangent vectors tensor Theorem Tºp topology trajectory transformation unique vector bundle vector field vector space velocity write