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arXiv · 2004.04622

Cartan Connection for Schr\"{o}dinger equation. The nature of vacuum

Radosław A. Kycia
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Abstract

We reinterpret the Schr\"{o}dinger equation as a continuity equation in the space with the Cartan connection given by scaling Lie-B\"{a}cklund 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 Schr\"{o}dinger-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.

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Radosław A. Kycia. 2020-04-09. Cartan Connection for Schr\"{o}dinger equation. The nature of vacuum. https://arxiv.org/abs/2004.04622

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