Conformal identities for invariant second-order variational problems depending on a covariant vector field

In this paper, necessary and sufficient conditions for the conformal invariance of a multiple integral variational problem whose Lagrangian depends upon second-order derivatives of a covariant vector field are obtained. These conditions take the form of differential identities involving the Lagrangian, its derivatives, and the infinitesimal generators of the special conformal group; they differ from the classical Noether identities in that they involve only second-order derivatives of the field, not fourth-order derivatives. The conditions are not conservation laws, but rather identities which provide a practical test for invariance which, if established, can lead to conservation laws via the Noether theorem. Finally, an application to 'generalised electrodynamics' is given. (author)