  The static potential in the confinement ``phase'' of the SU(2) Higgs model is
studied. In particular, the observation of the screening (called string
breaking) of the static quarks by the dynamical light quarks leading to the
formation of two static-light mesons was not observed before my work in
non-Abelian gauge theories. The tool that I employ is lattice gauge simulation.
The observable from which the spectrum of the Hamiltonian in presence of two
static quarks can be extracted, is a matrix correlation whose elements are
constructed not only from string-type states represented by Wilson loops (like
in pure gauge theories). Additional matrix elements representing transitions
from string-type to meson-type states and the propagation of meson-type states
are taken into account. From this basis of states it is possible to extract the
ground state and first excited state static potentials employing a variational
method. The crossing of these two energy levels in the string breaking region
is clearly visible and the inadequacy of the Wilson loops alone can be
demonstrated. I also address the question of the lattice artifacts. For this
purpose lines of constant physics in the confinement ``phase'' of the model
have to be constructed. This problem has only partially been solved.
Nevertheless it is possible to show that the static potentials have remarkable
scaling properties under a variation of the lattice spacing by a factor two and
are almost independent of the quartic Higgs coupling.
