Phys. Rev. D 51, 5498–5506 (1995)Reality conditions and Ashtekar variables: A different perspectiveReceived 13 October 1994; published in the issue dated 15 May 1995 We give in this paper a modified self-dual action that leads to the SO (3) ADM formalism without having to face the difficult second-class constraints present in other approaches (for example, if the starting point is the Hilbert-Palatini action). We use the new action principle to gain some new insight into the problem of the reality conditions that must be imposed in order to get real formulations from complex general relativity. We derive also a real formulation for Lorentzian general relativity in the Ashtekar phase space by using the modified action presented in the paper. © 1995 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.51.5498
DOI:
10.1103/PhysRevD.51.5498
PACS:
04.20.Cv, 04.20.Fy
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