  A candidate for a realistic relativistic quantum theory is the hypersurface
Bohm-Dirac model. Its formulation uses a foliation of spacetime into space-like
hypersurfaces. This structure may well arise from the universal wave function
itself, entailing the relativistic character of the theory despite the
appearance of a preferred foliation. However, to apply the theory and to make
contact with the usual quantum formalism one needs a framework for the
description of subsystems. The presence of spin together with the foliation
renders the subsystem description more complicated as compared to the
non-relativistic case with spin. In this paper, we provide such a framework in
terms of an appropriate conditional density matrix and an effective wave
function as well as clarify their relation, thereby generalizing previous
subsystem descriptions in the non-relativistic case.
