Conservation laws for non-global Lagrangians. (English) Zbl 1060.70034

Borowiec, A.; Ferraris, M.; Francaviglia, M.; Palese, M.

Zesz. Nauk. Uniw. Jagiell. 1269, Univ. Iagell. Acta Math. 41, 319-331 (2003).

Using symmetries and conservation laws of field theories, the authors study globality properties of conserved currents associated with non-global Lagrangians which admit global Euler-Lagrange morphisms. The basis is the geometric formulation of the calculus of variations on finite-order jets of fibered manifolds in terms of variational sequences. The authors prove the existence of global conserved quantities associated with Lagrangian symmetries and with generalized Lagrangian symmetries of Čech cochains of Lagrangians.

Reviewer: Andrew Bucki (Edmond)

MSC:

70S10	Symmetries and conservation laws in mechanics of particles and systems
70S05	Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
58Z05	Applications of global analysis to the sciences

Keywords:

fibered manifolds; variational sequences; global Euler-Lagrange morphisms