A relation of two and three-dimensional magnetic Weyl-Dirac operators

Based on ideas mainly developed in Erdős and Solovej, 2001 and Aharonov and Casher, 1979, we consider a certain class of magnetic potentials, whose corresponding magnetic field is parallel to a particular class of Conformal Killing Fields, and the related magnetic Dirac operators. We deduce an equation interlacing these Dirac operators on R3 with a class of Dirac operators on R2. In the process, we introduce a one-parameter family of typically non-Hausdorff coordinate spaces, on members of which we map R3 using a Riemann-type submersion and show that standard Differential Geometry results hold for such spaces too.