  Weyl quantization and related semiclassical techniques can be used to study
conduction properties of crystalline solids subjected to slowly-varying,
external electromagnetic fields. The case where the external magnetic field is
constant, is not covered by existing theory as proofs involving usual Weyl
calculus break down. This is the regime of the so-called quantum Hall effect
where quantization of transverse conductance is observed. To rigorously derive
semiclassical equations of motion, one needs to systematically develop a
magnetic Weyl calculus which contains a semiclassical parameter.
  Mathematically, the operators involved in the analysis are magnetic
pseudodifferential operators, a topic which by itself is of interest for the
mathematics and mathematical physics community alike. Hence, we will devote two
additional chapters to further understanding of properties of those operators.
