Local variational problems and conservation laws

摘要

We investigate globality properties of conserved currents associated with local variational problems admitting global Euler-Lagrange morphisms. We show that the obstruction to the existence of a global conserved current is the difference of two conceptually independent cohomology classes: one coming from using the symmetries of the Euler-Lagrange morphism and the other from the system of local Noether currents.