The reality conditions for the new canonical variables of General Relativity

Details The reality conditions for the new canonical variables of General Relativity The reality conditions for the new canonical variables of General Relativity

1992-02-20

arxiv.org/abs/hep-th/9202071v1

Class.Quant.Grav.10:2347-2352,1993

Physics

High Energy Physics

High Energy Physics - Theory

11 p

Scientific paper

10.1088/0264-9381/10/11/017

We examine the constraints and the reality conditions that have to be imposed in the canonical theory of 4--d gravity formulated in terms of Ashtekar variables. We find that the polynomial reality conditions are consistent with the constraints, and make the theory equivalent to Einstein's, as long as the inverse metric is not degenerate; when it is degenerate, reality conditions cannot be consistently imposed in general, and the theory describes complex general relativity.

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