Noether identities in Einstein--Dirac theory and the Lie derivative of spinor fields

Abstract

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.Comment: 11 pages, completely rewritten, contains an example of application to the coupling of gravity with spinors; in v4 misprints correcte