Abstract
The paraxial (parabolic) theory of a near forward scattering of a quantum charged 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 for two models: (i) Gaussian $\ensuremath{\delta}$-correlated random magnetic field; (ii) a random array of the Aharonov-Bohm magnetic flux line. The paraxial gauge-invariant two-particle Green function averaged with respect to the random magnetic field is found by an exact evaluation of the Feynman integral. It is shown that in spite of the anomalous character of the forward scattering, the transport properties can be described by the Boltzmann equation. The Landau quantization in the gauge field of the Aharonov-Bohm lines is discussed.
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