Geometric description of Schrödinger equation in Finsler and Funk geometry

Abstract

For a system of [Formula: see text] non-relativistic spinless bosons, we show by using a set of suitable matching conditions that the quantum equations in the pilot-wave limit can be translated into a geometric language for a Finslerian manifold. We further link these equations to Euclidean time-like relative Funk geometry and show that the two different metrics in both of these geometric frameworks lead to the same coupling.