Elektronen auf der Kugeloberfläche im magnetischen Monopolfeld : eine Untersuchung der Greensfunktion im White Noise Potential

The disorder averaged Greensfunction of non-interacting electrons in a strong magnetic field is investigated. First the known results for the plane are presented. Reduction to a zero- dimensional system enables to find the exact Greensfunction. The second part generalizes the plane to the surface of a sphere. The unperturbedproblem gives representations of SU(2) for the states of the electrons. Using the symmetries of these functions it is possible to construct the exact solution for upto 4 particles ; the density of states shows very good agreement with the result for N = $\infty$. Perturbative expansion is investigated for arbitrary particle numbers. Each diagram corresponds to a scalar, composed of Clebsch-Gordan-coefficients. In the limit of high energy the leading behavior of the Greensfunction can be isolated. Finally a perturbative expansion of the leading corrections to the result in the plane is given