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Unambiguous formalism for higher order Lagrangian field theories

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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.

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Please use this url to cite or link to this publication:

MLA
Campos, CM et al. “Unambiguous Formalism for Higher Order Lagrangian Field Theories.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 42.47 (2009): n. pag. Print.
APA
Campos, C., de Leon, M., de Diego, D., & Vankerschaver, J. (2009). Unambiguous formalism for higher order Lagrangian field theories. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 42(47).
Chicago author-date
Campos, CM, M de Leon, DM de Diego, and Joris Vankerschaver. 2009. “Unambiguous Formalism for Higher Order Lagrangian Field Theories.” Journal of Physics A-mathematical and Theoretical 42 (47).
Chicago author-date (all authors)
Campos, CM, M de Leon, DM de Diego, and Joris Vankerschaver. 2009. “Unambiguous Formalism for Higher Order Lagrangian Field Theories.” Journal of Physics A-mathematical and Theoretical 42 (47).
Vancouver
1.
Campos C, de Leon M, de Diego D, Vankerschaver J. Unambiguous formalism for higher order Lagrangian field theories. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2009;42(47).
IEEE
[1]
C. Campos, M. de Leon, D. de Diego, and J. Vankerschaver, “Unambiguous formalism for higher order Lagrangian field theories,” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 42, no. 47, 2009.
@article{889059,
  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.},
  author       = {Campos, CM and de Leon, M and de Diego, DM and Vankerschaver, Joris},
  issn         = {1751-8113},
  journal      = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
  language     = {eng},
  number       = {47},
  title        = {Unambiguous formalism for higher order Lagrangian field theories},
  url          = {http://dx.doi.org/10.1088/1751-8113/42/47/475207},
  volume       = {42},
  year         = {2009},
}

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