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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 1994

The prolongation formula for tensor fields

Satyanad Kichenassamy

Résumé

We derive a generalization of the prolongation formula for tensor-valued functions, by taking into account the natural action of diffeomorphisms on tensor fields. This differs from the usual procedure, where such fields are viewed as defining ``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.

Dates et versions

hal-00002649 , version 1 (20-08-2004)

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Satyanad Kichenassamy. The prolongation formula for tensor fields. Journal of Physics A: Mathematical and Theoretical, 1994, 27, pp.7857-7874. ⟨10.1088/0305-4470/27/23/029⟩. ⟨hal-00002649⟩
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