This is a contribution to the MG9 session QG1-a. A new quantum representation
for the Lorentzian gravity is created from the Pullin vaccum by the operators
assigned to 2-complexes. The representation uses the original, spinorial
Ashtekar variables, the reality conditions are well posed and Thiemann's
Hamiltonian is well defined. The results on the existence of a suitable Hilbert
product are partial. They were derived in collaboration with Abhay Ashtekar.Comment: QG1-a session of MG