Einstein-Dirac theory on gauge-natural bundles

TL;DR

This paper emphasizes the significance of gauge-natural bundles and Lie derivatives in classical field theory, revealing an unexpected indeterminacy in conserved quantities within Einstein-Cartan gravity coupled with Dirac fields.

Contribution

It demonstrates the importance of the functorial approach of gauge-natural bundles for formulating Einstein-Cartan gravity with Dirac fields, highlighting a novel indeterminacy in conserved quantities.

Findings

Highlighting the role of gauge-natural bundles in classical field theory

Identifying an unexpected indeterminacy in conserved quantities

Clarifying the geometrical formulation of Einstein-Cartan gravity with Dirac fields

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.