  The version of Bohmian mechanics in relativistic space-time that works best,
the hypersurface Bohm--Dirac model, assumes a preferred foliation of space-time
into spacelike hypersurfaces (called the time foliation) as given. We consider
here a degenerate case in which, contrary to the usual definition of a
foliation, several leaves of the time foliation have a region in common. That
is, if we think of the time foliation as a 1-parameter family of hypersurfaces,
with the hypersurfaces moving towards the future as we increase the parameter,
a degenerate time foliation is one for which a part of the hypersurface does
not move as we increase the parameter. We show that the hypersurface
Bohm--Dirac model still works in this situation; that is, we show that a
Bohm-type law of motion can still be defined, and that the appropriate
$|\psi|^2$ distribution is still equivariant with respect to this law.
