  It is a long-standing question whether the confinement of matter fields in
QCD has an imprint in the (gauge-dependent) correlation functions, especially
the propagators. As the analytic structure plays an important role in this
question, high-precision data is necessary for lattice investigations. Also, it
is interesting how this depends on the dimensionality of the theory. To make a
study over a wide range of parameters possible this suggests to use scalar
particles. This is done here: The propagator of a fundamental scalar is studied
in two, three, and four dimensions in quenched SU(2) Yang-Mills theory in
minimal Landau gauge, both in momentum space and position space. Particular
emphasis is put on the effects of renormalization. The results suggest a quite
intricate volume dependence and the presence of an intrinsic mass scale, but no
obvious connection to confinement.
