Noether's Second Theorem on natural bundles

Following work by Anderson, in this paper we present a formulation of Noether's Second Theorem that is valid on any natural bundle.

CLASSICAL GAUGE GRAVITATION THEORY

Classical gravitation theory is formulated as gauge theory on natural bundles where gauge symmetries are general covariant transformations and a gravitational field is a Higgs field responsible for their spontaneous symmetry breaking.

GAUGE-NATURAL NOETHER CURRENTS AND CONNECTION FIELDS

We study geometric aspects concerned with symmetries and conserved quantities in gauge-natural invariant variational problems and investigate implications of the existence of a reductive split structure associated with canonical Lagrangian conserved quantities on gauge-natural bundles. In particular, we characterize the existence of covariant conserved quantities in terms of principal Cartan connections on gauge-natural prolongations.