  We consider an electron coupled to a random magnetic field with local
correlations and eventually non-zero average value. Starting from the
source-term formalism of Levine, Libby and Pruisken, we define a generating
function for static transport coefficients. We use a non-hermitian
representation of the Hamiltonian, and a functionnal representation of the
generating function, where the integration variable consists of non-local
supermatrices, due to the non-locality of the Aharanov-Bohm interaction.The
conductivity coefficients are computed using a specific saddle-point procedure,
which incorporates ladder diagrams contributions. The situation with an
external uniform magnetic field is considered with the two different spin
projection possibilities. The limit of vanishingly small external magnetic
field is unstable with respect to spin flip, because of E=0 states. In
particular a quantized step is obtained when comparing the Hall conductance
between the two possible spin projections.
