The Prolongation Formula for Tensor Fields
نویسنده
چکیده
We derive a generalization of the prolongation formula for tensorvalued functions, by taking into account the natural action of di eomorphisms on tensor elds. This di ers from the usual procedure, where such elds are viewed as de ning \multi-component scalars;" it replaces the ordinary derivative in the expression of the \characteristic" by a Lie derivative. The resulting version of Noether's theorem takes a form closer to what is familiar to theoretical physicists. A very simple proof of the conformal invariance of the Maxwell Lagrangian also follows from this procedure. The Eshelby tensor is also readily obtained, as a further illustration of the practical use of this new prolongation formula.
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