Einstein-Dirac theory on gauge-natural bundles

Abstract

We present a clear-cut example of the importance of the functorial approach of gauge-natural bundles and the general theory of Lie derivatives for classical field theory, where the sole correct geometrical formulation of Einstein (-Cartan) gravity coupled with Dirac fields gives rise to an unexpected indeterminacy in the concept of conserved quantities.

LaTeX (20 pages, 2 runs). Enlarged introduction, corrected typos, updated references

References in corpus (3)

• Covariant theory of asymptotic symmetries, conservation laws and central charges
• Metric-affine gravity and the Nester-Witten 2-form
• Two-spinor Formulation of First Order Gravity coupled to Dirac Fields

Cited by in corpus (7)

• Multisymplectic formulation of vielbein gravity. De Donder-Weyl formulation, Hamiltonian (n-1)-forms
• Charges and Energy in Chern-Simons Theories and Lovelock Gravity
• The Lie derivative of spinor fields: theory and applications
• Covariant gauge-natural conservation laws
• Lagrangian reductive structures on gauge-natural bundles
• Generic Theory of Geometrodynamics from Noether's theorem for the Diff(M) symmetry group
• Gauge-natural field theories and Noether Theorems: canonical covariant conserved currents