## Noether's Theorems: Applications in Mechanics and Field TheoryThe book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory. |

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### Contents

1 | |

17 | |

3 Lagrangian and Hamiltonian Field Theories | 27 |

4 Lagrangian and Hamiltonian Nonrelativistic Mechanics | 58 |

5 Global Kepler Problem | 93 |

6 Calculus of Variations on Graded Bundles | 103 |

7 Noethers Second Theorems | 134 |

8 YangMills Gauge Theory on Principal Bundles | 163 |

11 ChernSimons Topological Field Theory | 201 |

12 Topological BF Theory | 207 |

Glossary | 211 |

Appendix ADifferential Calculus over Commutative Rings | 213 |

Appendix BDifferential Calculus on Fibre Bundles | 227 |

Appendix CCalculus on Sheaves | 259 |

Appendix DNoether Identities of Differential Operators | 271 |

References | 280 |

### Other editions - View all

Noether's Theorems: Applications in Mechanics and Field Theory Gennadi Sardanashvily No preview available - 2016 |

### Common terms and phrases

affine bundle bicomplex BRST bundle coordinates calculus called canonical commutative ring complex conservation law corresponding cotangent bundle covariant DBGA defined Definition differential operator Euler–Lagrange operator exact sequence exterior forms fibre bundle fibred manifold field theory form H gauge SUSY gauge symmetries global section graded bundle graded commutative graded commutative ring graded derivation graded Lagrangian Hamilton equation Hamiltonian form Hamiltonian system Hamiltonian vector fields integrals of motion isomorphism jet bundle jet order jet prolongation Jºº Lagrangian system Lagrangian theory Lemma Let us consider Lie algebra Lie derivative linear module monomorphism nilpotent Noether identities Noether’s nontrivial obeys order jet manifold order Lagrangian phase space presheaf principal bundle principal connection pull-back Remark Sardanashvily sheaf simple graded manifold structure subbundle submanifold symmetry current symplectic takes a form tangent bundle topological transition functions trivial variational formula vector bundle virtue of Theorem Yang–Mills