  The Zeeman-Hamilton operators of free charged particles are identified with
the Laplacians of certain Riemannian manifolds, called Zeeman manifolds. The
quantum Hilbert space decomposes into subspaces (Zeeman zones) which are
invariant under the actions both of the Zeeman operator and the natural
Heisenberg group representation. Thus a well defined particle theory and zonal
geometry can be developed on each zone separately. The most surprising result
is that quantities those divergent on the global setting appear to be finite on
the zonal setting. Even the zonal Feynman integral is well defined.
