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

$d \mathbf{L} = \mathbf{E} - d_H \theta$

for some form $\theta$. This $\mathbf{E}$ is the Euler-Lagrange form of $\mathbf{L}$.

G. J. Zuckerman, Action principles and global geometry , in Mathematical Aspects of String Theory, S. T. Yau (Ed.), World Scientific, Singapore, 1987, pp. 259€284. (pdf)

Last revised on November 30, 2017 at 12:34:07.
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