IJPAM: Volume 54, No. 2 (2009)


Michael Berg$^1$, Evert Jan Post$^2$, Hooman Rahimizadeh$^3$
$^{1,3}$Department of Mathematics
Loyola Marymount University
1 LMU Drive
Los Angeles, California, 90045-2659, USA
$^2$Department of Physics
University of Houston
4800, Calhoun Road
Houston, Texas, 77004, USA

Abstract.We propose that certain physical phenomena, that are currently dealt with by means of the formalism belonging to the Copenhagen interpretation of quantum mechanics, be dealt with, instead, using a path integral formalism auguring for the eventual introduction of de Rham cohomology. We lend support to our position by analyzing the Aharonov-Bohm experiment anew, by re-examining a theme (introduced by Kiehn) concerning Gauss-Ampère integrals, by revisiting a remark by Planck, and by introducing a parallel with Maxwell's equations. We go on to discuss various geometric and topological connections and their physical consequences.

Received: June 23, 2009

AMS Subject Classification: 35Q40, 14F40, 83C22

Key Words and Phrases: quantum mechanics, Rham cohomology, Aharonov-Bohm experiment, Gauss-Ampère integrals, Maxwell's equations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 2