Constraints and Reality Conditions in the Ashtekar Formulation of   General Relativity
  We show how to treat the constraints and reality conditions in the $SO(3)$-ADM (Ashtekar) formulation of general relativity, for the case of a vacuum spacetime with a cosmological constant. We clarify the difference between the reality conditions on the metric and on the triad. Assuming the triad reality condition, we find a new variable, allowing us to solve the gauge constraint equations and the reality conditions simultaneously. 
Gen Yoneda and Hisaaki Shinkai (Waseda University)