Given a smooth bundle , then a differential form on its jet bundle 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 itself (e.g. Zuckerman 87, p. 6):
Given a local Lagrangian , i.e. a horizontal form on of maximal horizontal degree, then there is a unique source form such that
for some form . This is the Euler-Lagrange form of .
The sum
is the corresponding Lepage form.
Last revised on September 14, 2023 at 17:59:08. See the history of this page for a list of all contributions to it.