Covariant gauge-natural conservation laws

Abstract

When a gauge-natural invariant variational principle is assigned, to determine {\em canonical} covariant conservation laws, the vertical part of gauge-natural lifts of infinitesimal principal automorphisms -- defining infinitesimal variations of sections of gauge-natural bundles -- must satisfy generalized Jacobi equations for the gauge-natural invariant Lagrangian. {\em Vice versa} all vertical parts of gauge-natural lifts of infinitesimal principal automorphisms which are in the kernel of generalized Jacobi morphisms are generators of canonical covariant currents and superpotentials. In particular, only a few gauge-natural lifts can be considered as {\em canonical} generators of covariant gauge-natural physical charges.

16 pages; presented at XXXVI Symposium on Math. Phys., Torun 09/06-12/06/04; the last paragraph of Section 3 has been reformulated, in particular a mistake in the equation governing the vertical part of gauge-natural lifts with respect to prolongations of principal connections (appearing e.g. in the vertical superpotential) has been corrected

References in corpus (3)

• The Hessian and Jacobi Morphisms for Higher Order Calculus of Variations
• Global Generalized Bianchi Identities for Invariant Variational Problems on Gauge-natural Bundles
• Generalized Bianchi identities in gauge-natural field theories and the curvature of variational principles

Cited by in corpus (11)

• Covariant Differential Identities and Conservation Laws in Metric-Torsion Theories of Gravitation. I. General Consideration
• Variationally equivalent problems and variations of Noether currents
• Lagrangian reductive structures on gauge-natural bundles
• Generalized Bianchi identities in gauge-natural field theories and the curvature of variational principles
• A variational perspective on classical Higgs fields in gauge-natural theories
• Cohomological obstructions in locally variational field theories
• Symmetries of Helmholtz forms and globally variational dynamical forms
• Second variational derivative of gauge-natural invariant Lagrangians and conservation laws
• Gauge-natural field theories and Noether Theorems: canonical covariant conserved currents
• The Jacobi morphism and the Hessian in higher order field theory; with applications to a Yang-Mills theory on a Minkowskian background
• Higgs fields induced by Yang--Mills type Lagrangians on gauge-natural prolongations of principal bundles