  Quantum field theory near thresholds of ultra-heavy particles is considered.
We focus especially on the top-antitop and the stop-antistop systems. The
question of the possible large corrections due to a running width of the top
quark could be solved in this work. It was shown that a previously not
considered contribution gives rise to large cancellations and leads especially
to a gauge independent result. With the help of a new zero order equation and a
Ward identity it was further possible to derive a general therorem for bound
state corrections to the width. Furthermore a systematic derivation of the
top-antitop and the stop-antistop potential to numerical order O(\alpha_s^4)
was given. In the second part of this work we consider within the numerical
Green function approach the cross sections for the production of ultraheavy
particles near threshold. The forward-backward asymmetry and the pure axial
contribution to the top-antitop total cross section as well as the
stop-antistop total cross section are calculated. A systematic method is given
to avoid unnatural cut-offs in the nonrelativistic treatment.
