CONSERVATIVE QUANTITIES AND THEIR ALGEBRA IN THE SELF-DUAL GRAVITY

A general covariant conservation law of energy-momentum in complex gen eral relativity is obtained by way of general displacement transformat ion in terms of Ashtekar's new variables. The energy is exactly the AD M Hamiltonian on the constraint surface on condition that an appropria te time function is chosen. The energy-momentum is gauge covariant and commutes with all the constraints whence they are physical observable s. Furthermore, the Poisson brackets of the momentum and the internal SU(2) charges form a 3-Poincare algebra.