  The usual quantization of a classical space-time field does not touch the
non-geometrical character of quantum mechanics. We believe that the deep
problems of unification of general relativity and quantum mechanics are rooted
in this poor understanding of the geometrical character of quantum mechanics.
In Einstein's theory gravitation is expressed by geometry of space-time, and
the solutions of the field equation are invariant w.r.t. a certain equivalence
class of reference frames. This class can be characterized by the differential
structure of space-time. We will show that matter is the transition between
reference frames that belong to different differential structures, that the set
of transitions of the differential structure is given by a Temperley-Lieb
algebra which is extensible to a $C^{*}$-algebra comprising the field operator
algebra of quantum mechanics and that the state space of quantum mechanics is
the linear space of the differential structures. Furthermore we are able to
explain the appearance of the complex numbers in quantum theory. The strong
relation to Loop Quantum Gravity is discussed in conclusion.
