Generalized Bianchi identities in gauge-natural field theories and the curvature of variational principles

TL;DR

This paper explores the relationship between generalized Bianchi identities and gauge-natural Jacobi morphisms, proposing a curvature concept for variational principles using Hamiltonian connections in gauge-natural field theories.

Contribution

It introduces a novel formulation linking Bianchi identities with gauge-natural Jacobi morphisms and defines a curvature for gauge-natural variational principles.

Findings

Bianchi identities relate to the kernel of gauge-natural Jacobi morphisms.

A new curvature concept for gauge-natural variational principles is proposed.

Hamiltonian connections are used to characterize the curvature in this framework.

Abstract

By resorting to Noether's Second Theorem, we relate the generalized Bianchi identities for Lagrangian field theories on gauge-natural bundles with the kernel of the associated gauge-natural Jacobi morphism. A suitable definition of the curvature of gauge-natural variational principles can be consequently formulated in terms of the Hamiltonian connection canonically associated with a generalized Lagrangian obtained by contracting field equations.