  Following our recent conjecture to model the phenomenona of
antiferromagnetism and superconductivity by quantum symmetry groups, we discuss
in the present note how to construct a workable scenario using this symmetry.
In particular we propose to patch the relevant critical points. This means we
identify fixed points, corresponding to various $k$ or $q$ [since the two are
related] and make expansion around these points, to control these expansion we
can impose gauge structure and we thus arrive at quantum group based gauge
theory or collection of classical gauge theories which represent the condensed
matter system such as cuprates. This is different than ordinary gauge theories
in several ways, for in ordinary field theory one has well-defined critical
point here the critical points are not unique or simple. In short the real
transition than in condensed matter system is represented by collection or {\it
ensemble average} of the several chosen critical points which come from
ordinary field theory [gauge theory].
  This idea may reveal the connection between Hubbard model and gauge theory
and string theory.
  In short it can lead to the non-perturbative formualtion of Hubbard and other
condensed matter Hamiltonians.
