  In this article we show in some detail how the full action functional of the
standard model of elementary particle physics can be described within the
geometrical setting of generalized Dirac operators. We thereby introduce a new
model building kit for (a certain class of) gauge invariant theories which
provides a unified geometrical description of Einstein's theory of gravity and
Yang-Mills gauge theories on the "classical" level. Moreover, when the gauge
symmetry is spontaneously broken, the Higgs sector as well has a natural
geometrical interpretation. It turns out that the Higgs field is related to the
gravitational potential.
  Since the full action functional of the standard model is derived in one
stroke, the appropriate parameters of the model have to satisfy certain
relations similar to those in the Connes-Lott approach. Likewise, this may
yield some phenomenological consequences, which is illustrated by using the
gauge group of the standard model in the case of $N-$generations of leptons and
quarks.
