Cartan Connection for Schrödinger equation. The nature of vacuum

Abstract

We reinterpret the Schrödinger equation as a continuity equation in the space with the Cartan connection given by scaling Lie-Bäcklund group on a specific jet space. In this space, the wave function and their gradient coordinates are treated as independent coordinates. This approach gives a full Cartan connection form a divergence-free condition. Once constructed, the connection makes it possible to investigate the geometry of the space on which this Schrödinger-Cartan connection is constructed. This is the idea that generalizes the concepts present in de Broglie-Bohm (pilot wave) theory in a geometric way. We also present this procedure for constructing (non-uniquely) torsion-free Cartan connections for general Partial Differential Equations.

14 pages