THE PROLONGATION FORMULA FOR TENSOR-FIELDS

We derive a generalization of the prolongation formula for tenser-valu ed functions, by taking into account the natural action of diffeomorph isms on tenser fields. This differs from the usual procedure, where su ch fields are viewed as defining 'multi-component scalars'; it replace s the ordinary derivative in the expression of the 'characteristic' by a Lie derivative. The resulting version of Noether's theorem takes a form more familiar to theoretical physicists. A very simple proof of t he conformal invariance of the Maxwell Lagrangian also follows from th is procedure. The Eshelby tenser is also readily obtained, as a furthe r illustration of the practical use of this new prolongation formula.