Displaying similar documents to “A new Lagrangian dynamic reduction in field theory”

Invariant variational problems on principal bundles and conservation laws

Ján Brajerčík (2011)

Archivum Mathematicum

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In this work, we consider variational problems defined by G -invariant Lagrangians on the r -jet prolongation of a principal bundle P , where G is the structure group of P . These problems can be also considered as defined on the associated bundle of the r -th order connections. The correspondence between the Euler-Lagrange equations for these variational problems and conservation laws is discussed.

Some geometric aspects of the calculus of variations in several independent variables

David Saunders (2010)

Communications in Mathematics

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This paper describes some recent research on parametric problems in the calculus of variations. It explains the relationship between these problems and the type of problem more usual in physics, where there is a given space of independent variables, and it gives an interpretation of the first variation formula in this context in terms of cohomology.

Some aspects of the homogeneous formalism in field theory and gauge invariance

Marcella Palese, Ekkehart Winterroth (2006)

Archivum Mathematicum

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We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended configuration bundle. This new approach can be interpreted as a suitable generalization to Field Theory of the homogeneous formalism for Hamiltonian Mechanics. As an example of application, we obtain the expression of a formal energy for a parametrized version...