Path-integral approach to the two-dimensional magneto-conductivity problem

We express Green's function and conductivity of an electron impurity system in the presence of a magnetic field or arbitrary strength in terms of Feynman path integrals and obtain an approximate formula for both the propagator and conductivity as the lowest order contribution of a systematic cumulant expansion. This approach takes the coherent scattering of an electron by impurity clusters at least approximately into account, in contrast to the self-consistent Born approximation (GBA) and similar approximations which are based on a partial summation of diagrams.In part II of this paper we apply this approach to a two-dimensional system, e.g. the surface channel of a field effect transistor, where the GBA leads to inconsistencies which arise from the discrete nature of the unperturbed energy spectrum in a quantizing magnetic field.