Three-Poincare Algebra in Complex General Relativity

We obtain a general covariant conservation law of energy momentum in complex general relativity by general displacement transformation in terms of Ashtekar new variables. The energy is exactly the ADM Hamiltonian on the constraint surface on condition that an appropriate time function is chosen. The energy momentum is gauge-covariant and commutes with all the constraints whence they are physical observables. Furthermore, the Poisson brackets of the momentum and the internal SU(2) charges form a three-Poincare algebra.