Paraxial propagation of a quantum charge in a random magnetic field

The paraxial (parabolic) theory of a near forward scattering of a quantum c harged particle by a static magnetic field is presented. From the paraxial solution to the Aharonov-Bohm scattering problem the transverse transferred momentum (the Lorentz force) is found. Multiple scattering is considered f or two models: (i) Gaussian S-correlated random magnetic field; (ii) a rand om array of the Aharonov-Bohm magnetic flux line. The paraxial gauge-invari ant two-particle Green function averaged with respect to the random magneti c field is found by an exact evaluation of the Feynman integral. It is show n that in spite of the anomalous character of the forward scattering, the t ransport properties can be described by the Boltzmann equation. The Landau quantization in the gauge field of the Aharonov-Bohm lines is discussed.