Gauge-natural field theories and Noether Theorems: canonical covariant conserved currents

Abstract

Recently we found that canonical gauge-natural superpotentials are obtained as global sections of the {\em reduced} $(n-2)$-degree and $(2s-1)$-order quotient sheaf on the fibered manifold $\bY_{\zet} \times_{\bX} \mathfrak{K}$, where $\mathfrak{K}$ is an appropriate subbundle of the vector bundle of (prolongations of) infinitesimal right-invariant automorphisms $\bar{\Xi }$. In this paper, we provide an alternative proof of the fact that the naturality property $\cL_{j_{s}\barΞ_{H}}ω(λ, \mathfrak{K})=0$ holds true for the {\em new} Lagrangian $\omega (\lambda ,\mathfrak{K})$ obtained contracting the Euler--Lagrange form of the original Lagrangian with ${\bar{\Xi }}_V\in \mathfrak{K}$. We use as fundamental tools an invariant decomposition formula of vertical morphisms due to Kolář and the theory of iterated Lie derivatives of sections of fibered bundles. As a consequence, we recover the existence of a canonical generalized energy--momentum conserved tensor density associated with $\omega (\lambda ,\mathfrak{K})$.

16 pages, abstract rewritten, body slightly revised, Proc. Winter School "Geometry and Physics" (Srni,CZ 2005)

References in corpus (7)

• Covariant gauge-natural conservation laws
• Noether's second theorem in a general setting. Reducible gauge theories
• The Hessian and Jacobi Morphisms for Higher Order Calculus of Variations
• Einstein-Dirac theory on gauge-natural bundles
• 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
• Space-time BRST symmetries