Unambiguous formalism for higher order Lagrangian field theories
Autor: | David Martín de Diego, Cédric M. Campos, Manuel de León, Joris Vankerschaver |
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Jazyk: | angličtina |
Rok vydání: | 2009 |
Předmět: |
Mathematics - Differential Geometry
Statistics and Probability 53C80 70S05 (Primary) 70H50 55R10 (Secondary) FOS: Physical sciences General Physics and Astronomy Legendre transformation Euler–Lagrange equation symbols.namesake Theoretical physics FOS: Mathematics Canonical form Legendre polynomials Mathematical Physics Mathematics Jet bundle Statistical and Nonlinear Physics Mathematical Physics (math-ph) Arbitrariness Differential Geometry (math.DG) Mathematics - Symplectic Geometry Modeling and Simulation symbols Symplectic Geometry (math.SG) Mathematics::Mathematical Physics Affine transformation Hamiltonian (quantum mechanics) |
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 |
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