  In this article, I discuss W.Kohn's criterion for a metal insulator
transition, within the framework of a one band Hubbard model. This and related
ideas are applied to 1-dimensional Hubbard systems, and some intersting
miscellaneous results discussed. The Jordan Wigner transformation converting
the two species of fermions to two species of hardcore bosons is performed in
detail, and the ``extra phases'' arising from odd-even effects are explicitly
derived. Bosons are shown to prefer zero flux (i.e. diamagnetism), and the
corresponding ``happy fluxes'' for the fermions identified. A curious result
following from the interplay between orbital diamagnetism and spin polarization
is highlighted.
  A ``spin-statistics'' like theorem, showing that the anticommutation
relations between fermions of opposite spin are crucial to obtain the SU(2)
invariance is pointed out.

Condensed Matter