Unambiguous formalism for higher order Lagrangian field theories

Autor: David Martín de Diego, Cédric M. Campos, Manuel de León, Joris Vankerschaver
Jazyk: angličtina
Rok vydání: 2009
Předmět:
Zdroj: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
ISSN: 1751-8113
Popis: 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, which 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 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.
Comment: 21 pages; 4 diagrams; (this version) corrected typos; moved paragraphs; published
Databáze: OpenAIRE