Abstract
In the paper the representation of the finite order variational sequence on fibered manifolds in field theory is studied. The representation problem is completely solved by a generalization of the integration by parts procedure using the concept of the Lie derivative of forms with respect to vector fields along canonical maps of prolongations of fibered manifolds. A close relationship between the obtained coordinate invariant representation of the variational sequence and some familiar objects of physics, such as Lagrangians, dynamical forms, Euler–Lagrange mapping and Helmholtz–Sonin mapping is pointed out and illustrated by examples.
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