  This paper addresses the problem of scattering line polarization and the
Hanle effect in one-dimensional (1D), two-dimensional (2D) and
three-dimensional (3D) media for the case of a two-level model atom without
lower-level polarization and assuming complete frequency redistribution. The
theoretical framework chosen for its formulation is the QED theory of Landi
Degl'Innocenti (1983), which specifies the excitation state of the atoms in
terms of the irreducible tensor components of the atomic density matrix. The
self-consistent values of these density-matrix elements is to be determined by
solving jointly the kinetic and radiative transfer equations for the Stokes
parameters. We show how to achieve this by generalizing to Non-LTE polarization
transfer the Jacobi-based ALI method of Olson et al. (1986) and the iterative
schemes based on Gauss-Seidel iteration of Trujillo Bueno and Fabiani Bendicho
(1995). These methods essentially maintain the simplicity of the
Lambda-iteration method, but their convergence rate is extremely high. Finally,
some 1D and 2D model calculations are presented that illustrate the effect of
horizontal atmospheric inhomogeneities on magnetic and non-magnetic resonance
line polarization signals.
