Noether identities in Einstein--Dirac theory and the Lie derivative of   spinor fields
  We characterize the Lie derivative of spinor fields from a variational point of view by resorting to the theory of the Lie derivative of sections of gauge-natural bundles. Noether identities from the gauge-natural invariance of the first variational derivative of the Einstein(--Cartan)--Dirac Lagrangian provide restrictions on the Lie derivative of fields. 
Marcella Palese, Ekkehart Winterroth (Dept. Math. Univ. Torino)