principle of extremal action, Euler-Lagrange equations, de Donder-Weyl formalism?
Given a smooth bundle $E \to \Sigma$, then a differential form on its jet bundle $J^\infty_\Sigma(E)$ is called a source form if it is of vertical degree 1 (with respect to the variational bicomplex) and its evaluation on a vector field depends only on the projection of that vector field to a vector field on $E$ itself (e.g. Zuckerman 87, p. 6):
Given a local Lagrangian $\mathbf{L}$, i.e. a horizontal form on $Jet(E)$ of maximal horizontal degree, then there is a unique source form $\mathbf{E}$ such that
for some form $\theta$. This $\mathbf{E}$ is the Euler-Lagrange form of $\mathbf{L}$.
The sum
is the corresponding Lepage form.
Last revised on November 30, 2017 at 07:34:07. See the history of this page for a list of all contributions to it.