Second variational derivative of local variational problems and conservation laws. (English) Zbl 1265.58008

Palese, Marcella; Winterroth, Ekkehart; Garrone, E.

Arch. Math., Brno 47, No. 5, 395-403 (2011).

The paper deals with topological aspects of conserved quantities which arise in correspondence of symmetries in field theories. Noether’s theorem is local in its nature; in the paper the more general problem of finding global conservation laws is addressed when there is no global Lagrangian to a given variational form.

Reviewer: Martin Čadek (Brno)

MSC:

58E30	Variational principles in infinite-dimensional spaces
55N30	Sheaf cohomology in algebraic topology
55R10	Fiber bundles in algebraic topology
58A12	de Rham theory in global analysis
58A20	Jets in global analysis

Keywords:

fibered manifold; jet space; Lagrangian formalism; variational sequence; second variational derivative; cohomology; symmetry; conservation law