Space–time transformation for the propagator in de Broglie–Bohm theory

Roderick I. Sutherland

Ciann‐Dong Yang

Jonáš Kulhánek

A. Tilbi, Tahar Boudjedaa, M. Merad +1 more

A calculation for the Kanai–Caldirola propagator in the de Broglie–Bohm theory is proposed. The technique of space-time transformations used in the Feynman path integral is adapted and then the problem is converted to that of the harmonic oscillator. The quantum propagator is viewed as an expansion of the guiding wave function over the velocity space. The construction is re-examined by replacing the integration over the initial velocity of the classic path by its final extremity. This gives a certain affinity with the Feynman path integral approach.

Domenico P. L. Castrigiano, F. Staerk

Jacob A. Barandes

The original version of the de Broglie-Bohm pilot-wave theory, also called Bohmian mechanics, attempted to treat the wave function or pilot wave as a part of the physical ontology of nature. More recent versions of the de Broglie-Bohm theory appearing in the last few decades have tried to regard the pilot wave instead as an aspect of the theory's nomology, or dynamical laws. This paper argues that neither of these views is correct, and that the de Broglie-Bohm pilot wave is best understood as a collection of latent variables in the sense of a hidden Markov model, a construct that was not available when de Broglie and Bohm originally formulated what became their pilot-wave theory. This paper also discusses several other challenges for the ontological view of the pilot wave. One such challenge is due to Foldy-Wouthuysen gauge transformations, which connect up with the Deotto-Ghirardi ambiguity in the de Broglie-Bohm theory. Another challenge arises from the freedom to carry out canonical transformations in the wave function's own notion of phase space, as defined by Strocchi and Heslot.