  We introduce the notion of Gauss-Landau-Hall magnetic field on a Riemannian
surface. The corresponding Landau-Hall problem is shown to be equivalent to the
dynamics of a massive boson. This allows one to view that problem as a globally
stated, variational one. In this framework, flowlines appear as critical points
of an action with density depending on the proper acceleration. Moreover, we
can study global stability of flowlines. In this equivalence, the massless
particle model correspond with a limit case obtained when the force of the
Gauss-Landau-Hall increases arbitrarily. We also obtain new properties related
with the completeness of flowlines for a general magnetic fields. The paper
also contains new results relative to the Landau-Hall problem associated with a
uniform magnetic field. For example, we characterize those revolution surfaces
whose parallels are all normal flowlines of a uniform magnetic field.
