The basic principles of geometrization of the quantum mechanics

TL;DR

This paper presents a geometric approach to quantum mechanics, deriving fundamental equations as wave equations on a manifold that encodes force interactions, based on a formalism extending de Broglie's postulate.

Contribution

It introduces a geometric formalism (K-field) that generalizes de Broglie's postulate, deriving core quantum equations as wave equations on a force-interaction manifold.

Findings

Quantum equations derived as wave equations on a geometric manifold

Force interactions modeled through geometric generalization

Provides a new geometric formulation of quantum mechanics

Abstract

The basic principles of the quantum mechanics in the K-field formalism (see author's papers) are stated in the paper. K-field formalism arises from geometric generalization of de Broglie postulate. So, the quantum theory equations (including well-known Schrodinger, Klein-Gordon and quadratic Dirac equations) are obtained as the free wave equations on a manifold metrizing force interactions of particles. In this paper, describing wave properties of particles we will restricted ourself with construction special geometric formulation of force interactions.