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We define a family of observables for abelian Yang-Mills fields associated to compact regions U ⊆ M with smooth boundary in Riemannian manifolds. Each observable is parametrized by a first variation of solutions and arises as the integration of gauge invariant conserved current along admissible hypersurfaces contained in the region. The Poisson bracket uses the integration of a canonical multisymplectic current.

By making use of the variational tricomplex, a covariant procedure is proposed for deriving the classical BRST charge from a given master-action. [ABSTRACT FROM AUTHOR]

Integrable equations with infinite hierarchies of symmetries are shown to arise in the context of the evolution of invariants of planar curves under geometric curve flows. A candidate for a recursion operator for these integrable equations arises naturally within the context of the computation of these evolution equations. The techniques of moving frames and the invariant variational bicomplex are used. [ABSTRACT FROM AUTHOR]

The construction of a finite-order bicomplex whose morphisms are the horizontal and vertical derivatives of differential forms on finite-order jet prolongations of fibered manifolds over one-dimensional bases is presented. In particular, relationship between the morphisms and classes entering the variational sequence and the associated finite-order bicomplex is studied. Properties of classes entering the infinite-order bicomplex, induced from the finite-order variational sequences by means of an infinite canonical construction, are formulated as a remark, insisting further research. [ABSTRACT FROM AUTHOR]

We define a family of observables for abelian Yang-Mills fields associated to compact regions U ⊆ M with smooth boundary in Riemannian manifolds. Each observable is parametrized by a first variation of solutions and arises as the integration of gauge invariant conserved current along admissible hypersurfaces contained in the region. The Poisson bracket uses the integration of a canonical multisymplectic current. [ABSTRACT FROM AUTHOR]