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Conservative Angular Momentum as SU(2) Charges in Complex Gravity

We obtain the conservative internal SU(2) charges in terms of Ashtekar new variables from the Lagrangian formalism of complex gravity. It is shown that the charges are related to the conservative angular momentum in the vierbein description of Einstein gravity and the Poisson brackets constitute the SU(2) algebra. Furthermore, they commute with all the constraints hence they are observable and expected to play an important role in the quantization of gravity.