Hamiltonian analysis of the double null 2+2 decomposition of General Relativity expressed in terms of self-dual bivectors

In this paper we obtain a 2+2 double null Hamiltonian description of General Relativity using only the (complex) SO(3) connection and the components of the complex densitised self-dual bivectors. We carry out the general canonical analysis of this system and obtain the first class constraint algebra entirely in terms of the self-dual variables. The first class algebra forms a Lie algebra and all the first class constraints have a simple geometrical interpretation.