Free Boundary Poisson Bracket Algebra in Ashtekar's Formalism

Details Free Boundary Poisson Bracket Algebra in Ashtekar's Formalism Free Boundary Poisson Bracket Algebra in Ashtekar's Formalism

1998-09-18

arxiv.org/abs/gr-qc/9809058v1

Theor.Math.Phys.112:906-921,1997; Teor.Mat.Fiz.112N1:142-160,1997

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, Latex, amsfonts.sty, amssymb.sty

Scientific paper

10.1007/BF02634107

We consider the algebra of spatial diffeomorphisms and gauge transformations in the canonical formalism of General Relativity in the Ashtekar and ADM variables. Modifying the Poisson bracket by including surface terms in accordance with our previous proposal allows us to consider all local functionals as differentiable. We show that closure of the algebra under consideration can be achieved by choosing surface terms in the expressions for the generators prior to imposing any boundary conditions. An essential point is that the Poisson structure in the Ashtekar formalism differs from the canonical one by boundary terms.

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