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Global Generalized Bianchi Identities for Invariant Variational Problems on Gauge-natural Bundles | | M. Palese
; E. Winterroth
; | | Date: |
5 Nov 2003 | | Journal: | Arch. Math. (Brno), 41(3) (2005) 289--310 | | Subject: | Mathematical Physics; Differential Geometry MSC-class: 58A20;58A32;58E30;58E40;58J10;58J70 | math-ph hep-th math.DG math.MP | | Affiliation: | Dept. Math. Univ. Torino, Italy | | Abstract: | We derive both {em local} and {em global} generalized {em Bianchi identities} for classical Lagrangian field theories on gauge-natural bundles. We show that globally defined generalized Bianchi identities can be found without the {em a priori} introduction of a connection. The proof is based on a {em global} decomposition of the {em variational Lie derivative} of the generalized Euler--Lagrange morphism and the representation of the corresponding generalized Jacobi morphism on gauge-natural bundles. In particular, we show that {em within} a gauge-natural invariant Lagrangian variational principle, the gauge-natural lift of infinitesimal principal automorphism {em is not} intrinsically arbitrary. As a consequence the existence of {em canonical} global superpotentials for gauge-natural Noether conserved currents is proved without resorting to additional structures. | | Source: | arXiv, math-ph/0311003 | | Services: | Forum | Review | PDF | Favorites | |
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