TY - JOUR UR - http://lib.ugent.be/catalog/pug01:889059 ID - pug01:889059 LA - eng TI - Unambiguous formalism for higher order Lagrangian field theories PY - 2009 JO - (2009) JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL SN - 1751-8113 PB - 2009 AU - Campos, CM AU - de Leon, M AU - de Diego, DM AU - Vankerschaver, Joris WE01 001999061882 AB - 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. ER -Download RIS file
| 00000nam^a2200301^i^4500 | |||
| 001 | 889059 | ||
| 005 | 20161219154430.0 | ||
| 008 | 100303s2009------------------------eng-- | ||
| 022 | a 1751-8113 | ||
| 024 | a 000271900200020 2 wos | ||
| 024 | a 1854/LU-889059 2 handle | ||
| 024 | a 10.1088/1751-8113/42/47/475207 2 doi | ||
| 040 | a UGent | ||
| 245 | a Unambiguous formalism for higher order Lagrangian field theories | ||
| 260 | c 2009 | ||
| 520 | a 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. | ||
| 598 | a A1 | ||
| 100 | a Campos, CM | ||
| 700 | a de Leon, M | ||
| 700 | a de Diego, DM | ||
| 700 | a Vankerschaver, Joris u WE01 0 001999061882 0 801001781625 | ||
| 773 | t JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL g J. Phys. A-Math. Theor. 2009. 42 (47) q 42:47< | ||
| 856 | 3 Full Text u https://biblio.ugent.be/publication/889059/file/889068 z [open] y paper.pdf | ||
| 920 | a article | ||
| 852 | x WE b WE01 | ||
| 922 | a UGENT-WE | ||
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