The Part VII deals with the first Noether theorem. It takes into account not only the first derivatives of the fields by the coordinates in Lagrangian, but also the second (this permits to apply this theorem to gravity, since the second derivatives from the metric tensor enter in the Lagrangian of the gravitational field).
Also this theorem is generalized on the curved spaces.
And at last it's generalized on asymmetric metric tensors.
The starting point for these generalizations was the book: Bogoliubov N.N., Shirkov D.V. Introduction to the theory of quantized fields (Wiley, 1980)(ISBN 0471042234)(600dpi)(T)(637s)_PQft_.djvuBack