  The definition of a positive energy is investigated in a renormalizable
4-dimensional generally covariant model, which depends on the lorentzian
complex structure and not the metric of spacetime. The gravitational content of
the lorentzian complex structures is revealed by identifying the spacetime with
special 4-dimensional surfaces of the G{2,2} Grassmannian manifold. The
lorentzian complex structure is found to be a codimension-4 CR structure and
its classification is studied using the Chern-Moser and Cartan methods. The
spacetime metric is found to be a Fefferman-like metric of this codimension-4
CR structure. The open CR manifolds "hanging" from the points of the U(2)
characteristic boundary of the SU(2,2) classical domain belong into
representations of the Poincar\'e group and are related to the particle
spectrum of the model.
