Quantum mechanics on Riemannian Manifold in Schwinger's Quantization Approach II

Extended Schwinger's quantization procedure is used for constructing quantum mechanics on a manifold with a group structure. The considered manifold $M$ is a homogeneous Riemannian space with the given action of isometry transformation group. Using the identification of $M$ with the quotient space $G/H$, where $H$ is the isotropy group of an arbitrary fixed point of $M$, we show that quantum mechanics on $G/H$ possesses a gauge structure, described by the gauge potential that is the connection 1-form of the principal fiber bundle $G(G/H, H)$. The coordinate representation of quantum mechanics and the procedure for selecting the physical sector of states are developed.Comment: 18pages, no figures, LaTe

Electron-electron interaction in carbon nanostructures

The electron-electron interaction in carbon nanostructures was studied. A new method which allows to determine the electron-electron interaction constant $\lambda_c$ from the analysis of quantum correction to the magnetic susceptibility and the magnetoresistance was developed. Three types of carbon materials: arc-produced multiwalled carbon nanotubes (arc-MWNTs), CVD-produced catalytic multiwalled carbon nanotubes (c-MWNTs) and pyrolytic carbon were used for investigation. We found that $\lambda_c$=0.2 for arc-MWNTs (before and after bromination treatment); $\lambda_c$ = 0.1 for pyrolytic graphite; $\lambda_c >$ 0 for c-MWNTs. We conclude that the curvature of graphene layers in carbon nanostructures leads to the increase of the electron-electron interaction constant $\lambda_c$.Comment: 12 pages, 18 figures, to be published in the Proceedings of the NATO Advanced Research Workshop on Electron Correlation in New Materials and Nanosystems, NATO Science Series II, Springer, 200