Abstract. The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner–Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler–Lagrange equations for higher order field theories. Several examples illustrate our construction.

PACS numbers: 03.50.−z, 02.40.Yy, 11.10.Ef

Mathematics Subject Classification: 70S05, 70H50, 53C80, 55R10

Print publication: Issue 47 (27 November 2009)
Received 30 June 2009, in final form 22 September 2009
Published 6 November 2009