Second variational derivative of gauge-natural invariant Lagrangians and conservation laws
Abstract
We consider the second variational derivative of a given gauge-natural invariant Lagrangian taken with respect to (prolongations of) vertical parts of gauge-natural lifts of infinitesimal principal automorphisms. By requiring such a second variational derivative to vanish, {\em via} the Second Noether Theorem we find that a covariant strongly conserved current is canonically associated with the deformed Lagrangian obtained by contracting Euler--Lagrange equations of the original Lagrangian with (prolongations of) vertical parts of gauge-natural lifts of infinitesimal principal automorphisms lying in the kernel of the generalized gauge-natural Jacobi morphism.
Keywords
Cite
@article{arxiv.math-ph/0411026,
title = {Second variational derivative of gauge-natural invariant Lagrangians and conservation laws},
author = {M. Francaviglia and M. Palese and E. Winterroth},
journal= {arXiv preprint arXiv:math-ph/0411026},
year = {2007}
}
Comments
17 pages; some misprints corrected, few changes, reference list updated, v3 to appear in Proc. IX Int. Conf. on Diff. Geom. and its Appl. (Prague 30/08-03/09/2004)