caa a22 4500 469031662 CHVBK 20180323132745.0 cr unu---uuuuu 170328e19920401xx s 000 0 eng 10.1007/BF00732924 doi (NATIONALLICENCE)springer-10.1007/BF00732924 Castro Carlos Center for Particle Theory, Physics Department, University of Texas at Austin, 78712, Austin, Texas aut On Weyl geometry, random processes, and geometric quantum mechanics [Elektronische Daten] [Carlos Castro] 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, $$m(R)\frac{{dm(R)}}{{dR}} = \frac{{\hbar ^2 }}{{c^2 }}$$ 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 prediction of this theory yields a 3×10−35 eV correction to the ground-state energy of the hydrogen atom. Plenum Publishing Corporation, 1992 Foundations of Physics Kluwer Academic Publishers-Plenum Publishers 22/4(1992-04-01), 569-615 0015-9018 22:4<569 1992 22 10701 https://doi.org/10.1007/BF00732924 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00732924 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Castro Carlos Center for Particle Theory, Physics Department, University of Texas at Austin, 78712, Austin, Texas aut NATIONALLICENCE 773 0- Foundations of Physics Kluwer Academic Publishers-Plenum Publishers 22/4(1992-04-01), 569-615 0015-9018 22:4<569 1992 22 10701 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer