Bohmian Mechanics for a Degenerate Time Foliation

Abstract

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.

13 pages LaTeX, 8 figures

References in corpus (4)

• Bohmian Mechanics and Quantum Field Theory
• Can Bohmian mechanics be made relativistic?
• Multi-Time Wave Functions for Quantum Field Theory
• Bohmian Trajectories For a Time Foliation with Kinks

Cited by in corpus (2)

• On Bohmian Mechanics, Particle Creation, and Relativistic Space-Time: Happy 100th Birthday, David Bohm!
• Consequences of a Two-Time Relativistic Bohmian Model