Poisson algebra independent on boundary conditions in Ashtekar's formalism

The algebra of spatial diffeomorfisms and gauge transformations is studied in the canonical formalism of General Relativity in Ashtekar and ADM variables. The previously proposed modification of a Poisson bracket by adding surface terms is exploited. It permits to consider all local functionals as admissible. It is shown that this algebra can be closed even before the fixing of boundary conditions due to a special choice of surface terms in the generators. The essential point is that the Poisson structure for the Ashtekar variables is not canonical on the boundary.