Wave function as geometric entity

TL;DR

This paper introduces a geometric approach to electron wave functions using Clifford numbers, deriving a Dirac-like equation applicable to any manifold, and discusses experimental implications of this geometric perspective.

Contribution

It presents a novel geometric representation of electron wave functions via Clifford numbers and derives a corresponding Dirac-like equation for arbitrary manifolds.

Findings

Derived a Dirac-like equation for geometric wave functions

Proposed experiments to test geometric nature of electrons

Demonstrated interference effects with geometric wave functions

Abstract

A new approach to the geometrization of the electron theory is proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any manifold. A solution of this equation is obtained in terms of geometric treatment. Interference of electrons whose wave functions are represented by geometric entities is considered. New experiments concerning the geometric nature of electrons are proposed.