New Approach to the Noether Theorems

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Abstract
The Noether theorems were derived by Noether for n‐dimensional Euclidean spaces, but they have been used by many writers in relativistic theories where the geometry is not Euclidean. We give a derivation of the Noether theorems, assuming only a Riemannian space and following the method used by Noether as closely as possible. This requires new definitions of total variations for fields and integrals since a covariant total variation for tensor fields is required. The results have been applied to electromagnetic fields.

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