When a gauge-natural invariant variational principle is assigned, to determine 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. 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 canonical generators of covariant gauge-natural physical charges.
Covariant gauge-natural conservation laws
PALESE, Marcella;WINTERROTH, Ekkehart Hans Konrad
2004-01-01
Abstract
When a gauge-natural invariant variational principle is assigned, to determine 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. 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 canonical generators of covariant gauge-natural physical charges.
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