Hypersurface Bohm-Dirac models

We define a class of Lorentz-invariant Bohmian quantum models for N entangl ed but noninteracting Dirac particles. Lorentz invariance is achieved for t hese models through the incorporation of an additional dynamical space-time structure provided by a foliation of space time. These models can be regar ded as the extension of Bohm's model for N Dirac particles, corresponding t o the foliation into the equal-time hyperplanes for a distinguished Lorentz frame, to more general foliations. As with Bohm's model, there exists for these models an equivariant measure on the leaves of the foliation. This ma kes possible a simple statistical analysis of position correlations analogo us to the equilibrium analysis for (the nonrelativistic) Bohmian mechanics. [S1050-2947(99)07910-X].