General Relativity as a Theory of Two Connections

Abstract

We show in this paper that it is possible to formulate General Relativity in a phase space coordinatized by two $SO(3)$ connections. We analyze first the Husain-Kuchař model and find a two connection description for it. Introducing a suitable scalar constraint in this phase space we get a Hamiltonian formulation of gravity that is close to the Ashtekar one, from which it is derived, but has some interesting features of its own. Among them a possible mechanism for dealing with the degenerate metrics and a neat way of writing the constraints of General Relativity.

18 pages, LATEX, Preprint CGPG-93/09-5

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