The Dirac-Bohm Picture

TL;DR

The paper introduces the Dirac-Bohm picture, a new quantum framework unitarily equivalent to Schrödinger and Heisenberg pictures, linking Bohm trajectories to Feynman paths.

Contribution

It establishes a new quantum picture derived from Dirac's algebraic approach, connecting Bohm trajectories with Feynman path integrals.

Findings

The Dirac-Bohm picture is unitarily equivalent to existing quantum pictures.

Bohm trajectories are shown to be averages over Feynman paths.

Provides a new perspective on quantum dynamics and interpretations.

Abstract

We examine Dirac's early algebraic approach which introduces the {\em standard} ket and show that it emerges more clearly from a unitary transformation of the operators based on the action. This establishes a new picture that is unitarily equivalent to both the Schr\"{o}dinger and Heisenberg pictures. We will call this the Dirac-Bohm picture for the reasons we discuss in the paper. This picture forms the basis of the Feynman path theory and allows us to show that the so-called `Bohm trajectories' are averages of an ensemble of Feynman paths.