Cohomological obstructions in locally variational field theories

Abstract

We study cohomological obstructions to the existence of global conserved quantities. In particular, we show that, if a given local variational problem is supposed to admit global solutions, certain cohomology classes cannot appear as obstructions. Vice versa, we obtain a new type of cohomological obstruction to the existence of global solutions for a variational problem.

9 pages, presented at the XXI Int. Conf. on Integrable Systems and Quantum Symmetries, ISQS-21, Prague, June 12-16 2013

References in corpus (5)

• Global Generalized Bianchi Identities for Invariant Variational Problems on Gauge-natural Bundles
• Variationally equivalent problems and variations of Noether currents
• Conservation laws for non global Lagrangians
• Second variational derivative of gauge-natural invariant Lagrangians and conservation laws
• Field equations or conservation laws?

Cited by in corpus (2)

• Topological obstructions in Lagrangian field theories, with an application to 3D Chern-Simons gauge theory
• Variational derivatives in locally Lagrangian field theories and Noether--Bessel-Hagen currents