Symmetry transformations of extremals and higher conserved quantities: invariant Yang--Mills connections
arXiv:1910.11688 · doi:10.1063/5.0038533
Abstract
We characterize symmetry transformations of Lagrangian extremals generating `on shell' conservation laws. We relate symmetry transformations of extremals to Jacobi fields and study symmetries of higher variations by proving that a pair given by a symmetry of the -th variation of a Lagrangian and by a Jacobi field of the -th variation of the same Lagrangian (with ) is associated with an `off shell' conserved current. The conserved current associated with two symmetry transformations is constructed and, as a case of study, its expression for invariant Yang--Mills connections on Minkowski space-times is obtained.
arXiv comment24 pages, title slightly changed, text expanded and improved, higher variations included, v4: some oversights corrected
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