  The coupling to a 2+1 background geometry of a quantized charged test
particle in a strong magnetic field is analyzed. Canonical operators adapting
to the fast and slow freedoms produce a natural expansion in the inverse square
root of the magnetic field strength. The fast freedom is solved to the second
order.
  At any given time, space is parameterized by a couple of conjugate operators
and effectively behaves as the `phase space' of the slow freedom. The slow
Hamiltonian depends on the magnetic field norm, its covariant derivatives, the
scalar curvature and presents a peculiar coupling with the spin-connection.
