3-POINCARE ALGEBRA IN COMPLEX GENERAL-RELATIVITY

We obtain a general covariant conservation law of energy momentum in c omplex general relativity by general displacement transformation in te rms of Ashtekar new variables. The energy is exactly the ADM Hamiltoni an on the constraint surface on conditions that an appropriate time fu nction is chosen. The energy momentum is gauge-covariant and commutes with all the constraints whence they are physical observables. Further more, the Poisson brackets of the momentum and the internal SU(2) char ges form a three-Poincare algebra.