The Canonical Symmetry and Hamiltonian Formalism. II. Hamiltonian Operators

It is shown how the canonical symmetry is used to look for the hierarchy of the Hamiltonian operators relevant to the system under consideration. It appears that only the invariance condition can be used to solve the problem.Comment: 13 pages, LaTeX file, IHEP 93-6

Hopf solitons and area preserving diffeomorphisms of the sphere

We consider a (3+1)-dimensional local field theory defined on the sphere. The model possesses exact soliton solutions with non trivial Hopf topological charges, and infinite number of local conserved currents. We show that the Poisson bracket algebra of the corresponding charges is isomorphic to that of the area preserving diffeomorphisms of the sphere. We also show that the conserved currents under consideration are the Noether currents associated to the invariance of the Lagrangian under that infinite group of diffeomorphisms. We indicate possible generalizations of the model.Comment: 6 pages, LaTe