Relativistic-covariant Bohmian mechanics with proper foliation

Abstract

In classical relativistic mechanics, a "preferred" proper direction in spacetime for each particle is determined by the direction of its 4-momentum. Analogously, for each quantum particle we find a local direction uniquely determined by the many-particle wave function, which for each particle defines the proper foliation of spacetime. This can be used to formulate a relativistic-covariant version of Bohmian mechanics, with equivariant probability density on proper hypersurfaces.

4 pages, Eqs. (25), (27) and (28) rewritten with a redefined sign factor, comment on related literature added