Stress-energy-momentum tensors in higher order variational calculus

Given a variational problem defined by a natural Lagrangian density Lw on t he k-jet extension J(k)(Y/X) of a natural bundle p : Y --> X over an n-dime nsional manifold X, oriented by a volume element w, a stress-energy-momentu m tensor T(s) is constructed for each section s is an element of Gamma(X, Y ) from the multimomentum map mu(Theta) : Gamma(X, Y) --> Hom(R)(H(X), Ohm(n -1)(X)) associated to any Poincare-Cartan form Theta and to the natural lif ting of vector fields H(X) to the bundle Y --> X. The characterization made for T(s) gives an intrinsic expression of this tensor as well as a general ization of the classical Belinfante-Rosenfeld formula. This tensor satisfie s the typical properties of a stress-energy-momentum tensor: Diff(X)-covari ance, Hilbert formula, conservation law, etc. Furthermore, it plays the exp ected role in the theory of minimal gravitational interactions. (C) 2000 El sevier Science B.V. All rights reserved. Subj. Class.: Classical field theo ry 1991 MSC: 58B30; 83C40; 76M30.