Abstract
A generalized Noether theorem is presented, relating symmetries and (equivalence classes of local) conservation laws in classical field theories; this is contrasted with the standard theorem. The concept of a “Noether” field theory is introduced, being a theory for which the generalized theorem applies; not only does this include the cases of Lagrangian and Hamiltonian field theories, these structures are “derived” from the Noether property in a natural way. The generalized theorem applies to currents and symmetries that contain derivatives of the fields up to an arbitrarily high order.
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