## The Noether theorem and independence of conserved quantities in Lagrangian field theories |

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### Contents

Lagrangian Theory on Jet Bundles | 6 |

Properties of the Cartan Form | 11 |

The Independence Conditions for Conserved Quantities | 14 |

10 other sections not shown

### Common terms and phrases

additional conserved quantities c-independent canonical coordinate system Cartan form Cartan ideal charged massive scalar choose component consider contact forms contact ideal converse Noether theorem critical sections definition of independence differential ideal Dirac field Dirac system drdt dsdx dxdt example exterior derivatives field without charge Foldy-Woutheysen geodesic motion hence ideal form Independence of Conserved independent conserved quantities independent Noetherian conserved jet bundle formulation jet bundle J(E Jr(E KdV system Klein-Gordon field Lagrange forms Lagrangian density Lagrangian field theory Lagrangian systems Lagrangian Theory massive scalar field massless Math maximal independent set maximal number maximal set Minkowski spacetime mod f(a Noetherian conserved quantities Noetherian symmetry currents nonlocal conserved quantities number of independent order jet bundle Phys result set of conserved solution ideal solution sections space symmetry vector field systems formulated test particle trivial conserved quantity variational principle variational systems vector bundle Weyl