Noether identities in Einstein--Dirac theory and the Lie derivative of spinor fields
Marcella Palese, Ekkehart Winterroth (Dept. Math. Univ. Torino)
TL;DR
This paper investigates the Lie derivative of spinor fields within Einstein--Dirac theory using variational methods and gauge-natural bundle theory, revealing restrictions from Noether identities related to gauge invariance.
Contribution
It introduces a variational characterization of the Lie derivative of spinor fields and links it to Noether identities in Einstein--Dirac theory, advancing understanding of gauge-natural invariance.
Findings
Derived restrictions on the Lie derivative of spinor fields from Noether identities.
Connected gauge-natural invariance with the variational behavior of spinor fields.
Provided a new variational perspective on the Lie derivative in Einstein--Dirac theory.
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.
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