Path-integral quantization of Kaluza-Klein monopole systems.

Abstract

A particle bound in the Kaluza-Klein monopole field (the static Taub-Newman-Unti-Tamburino space) is quantized by path integration. First, the system is regularized by the Kustaanheimo-Stiefel procedure. Then, path integration is performed in the Euler variables to separate the monopole harmonics. Dirac's charge quantization condition is deduced naturally by dimensional reduction. The radial path integral leads to the radial Green's function expressed in closed form, from which the discrete energy spectrum for {ital g}{lt}0 ({ital g}=4{ital m} is the monopole parameter) and the corresponding wave functions are obtained. A possibility of creating bound states for {ital g}{gt}0 is also discussed by introducing an external Coulomb-like potential.