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.
Physical Review D
- Pub Date:
- May 1995
- Fundamental problems and general formalism;
- Canonical formalism Lagrangians and variational principles;
- General Relativity and Quantum Cosmology
- 22 pages, LATEX, Preprint CGPG-94/10-2