On Weyl geometry, random processes, and geometric quantum mechanics

Abstract:

This paper discusses some of the technical problems related to a Weylian geometrical interpretation of the Schrödinger and Klein-Gordon equations proposed by E. Santamato. Solutions to these technical problems are proposed. A general prescription for finding out the interdependence between a particle's effective mass and Weyl's scalar curvature is presented which leads to the fundamental equation of geometric quantum mechanics, {Mathematical expression} The Dirac equation is rigorously derived within this formulation, and further problems to be solved are proposed in the conclusion. The main one is based on obtaining the relationship between Feynman's path integral quantization method, among others, and the methods of geometric quantum mechanics. The solution of this problem will be a crucial test for this theory that attempts to "geometrize" quantum mechanics rather than the conventional approach in the past of quantizing geometry. A numerical pbkp_rediction of this theory yields a 3×10-35 eV correction to the ground-state energy of the hydrogen atom. © 1992 Plenum Publishing Corporation.

Año de publicación:

1992

Keywords:

Fuente:

scopus