A relativistically covariant version of Bohm's quantum field theory for the scalar field

We give a relativistically covariant, wave-functional formulation of Bohm's quantum field theory for the scalar field based on a general foliation of spacetime by space-like hypersurfaces. The wave functional, which guides the evolution of the field, is spacetime-foliation independent but the field itself is not. Hence, in order to have a theory in which the field may be considered a beable, some extra rule must be given to determine the foliation. We suggest one such rule based on the eigenvectors of the energy–momentum tensor of the field itself.