Reality Conditions and Ashtekar Variables: a Different Perspective

Details Reality Conditions and Ashtekar Variables: a Different Perspective Reality Conditions and Ashtekar Variables: a Different Perspective

1994-10-11

arxiv.org/abs/gr-qc/9410013v1

Phys.Rev.D51:5498-5506,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, LATEX, Preprint CGPG-94/10-2

Scientific paper

10.1103/PhysRevD.51.5498

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 one starts from the Hilbert-Palatini action). We use the new action principle to gain some new insights 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.

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