Covariant gauge-natural conservation laws. (English) Zbl 1066.58009

Palese, M.; Winterroth, E.

Rep. Math. Phys. 54, No. 3, 349-364 (2004).

Summary: When a gauge-natural invariant variational principle is assigned, to determine canonical covariant conservation laws, the vertical part of gauge-natural lifts of infinitesimal principal automorphisms – defining infinitesimal variations of sections of gauge-natural bundles – must satisfy generalized Jacobi equations for the gauge-natural invariant Lagrangian. Vice versa all vertical parts of gauge-natural lifts of infinitesimal principal automorphisms which are in the kernel of generalized Jacobi morphisms are generators of canonical covariant currents and superpotentials. In particular, only a few gauge-natural lifts can be considered as canonical generators of covariant gauge-natural physical charges.

MSC:

58E30	Variational principles in infinite-dimensional spaces
58A20	Jets in global analysis
70S10	Symmetries and conservation laws in mechanics of particles and systems
70S05	Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
58A32	Natural bundles
58E40	Variational aspects of group actions in infinite-dimensional spaces

Keywords:

gauge-natural bundles; invariant variational principles; variational sequences; generalized Jacobi morphisms; conservation laws

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