Abstract
A quantal guiding centre theory is presented which allows a systematical study of the separation of the different time scale behaviours of a quantum charged spinning particle moving in an external inhomogeneous magnetic field. A suitable set of operators adapting to the canonical structure of the problem and generalizing the kinematical momenta and guiding centre operators of a particle coupled to a homogeneous magnetic field is constructed. This allows us to rewrite the Pauli Hamiltonian as a power series in the magnetic length making the problem amenable to a perturbative analysis. The first two terms of the series are explicitly constructed. The effective adiabatic dynamics turns out to be in coupling with a gauge field and a scalar potential. The mechanism producing such magnetic-induced geometric-magnetism is investigated in some detail.
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