  According to the introduction of a minimal length to quantum field theory
which is directly related to a generalized uncertainty principle the
implementation of the gauge principle becomes much more intricated. It has been
shown in another paper how gauge theories have to be extended in general, if
there is assumed the existence of a minimal length. In this paper this
generalization of the description of gauge theories is applied to the case of
Yang-Mills theories with gauge group SU(N) to consider especially the
application to the electroweak theory as it appears in the standard model. The
modifications of the lepton-, Higgs- and gauge field sector of the extended
Lagrangian of the electroweak theory maintaining local gauge invariance under
$SU(2)_L\otimes U(1)_Y$ transformations are investigated. There appear
additional interaction terms between the leptons or the Higgs particle
respectively with the photon and the W- and Z-bosons as well as additional
self-interaction terms of these gauge bosons themselves. It is remarkable that
in the quark sector where the full gauge group of the standard model, $SU(3)_c
\otimes SU(2)_L\otimes U(1)_Y$, has to be considered there arise coupling terms
between the gluons und the W- and Z-bosons which means that the electroweak
theory is not separated from quantum chromodynamics anymore.
