  There is considered an extension of gauge theories according to the
assumption of a generalized uncertainty principle which implies a minimal
length scale. A modification of the usual uncertainty principle implies an
extended shape of matter field equations like the Dirac equation. If there is
postulated invariance of such a generalized field equation under local gauge
transformations, the usual covariant derivative containing the gauge potential
has to be replaced by a generalized covariant derivative. This leads to a
generalized interaction between the matter field and the gauge field as well as
to an additional self interaction of the gauge field. Since the existence of a
minimal length scale seems to be a necessary assumption of any consistent
quantum theory of gravity, the gauge principle is a constitutive ingredient of
the standard model and even gravity can be described as gauge theory of local
translations or Lorentz transformations, the presented extension of gauge
theories appears as a very important consideration.
