The Propagation of Quarks in the Spatial Direction in Hot QCD

The dynamics of {\it light} fermions propagating in a spatial direction at high temperatures can be described effectively by a two--dimensional Schr\"odinger equation with {\it heavy} effective mass $m_{\rm eff} = \pi T$. Starting from QED, we discuss the transition from three-- to two--dimensional positronium discussing the latter in detail including relativistic effects. In the case of QCD the problem is similar to that of heavy quarkonium. Our effective potential contains the usual Coulomb and confining parts as well as a perturbative spin--spin interaction. The resulting $\bar q q$ ``wave functions" reproduce recent lattice data for the $\rho$ and $\pi$ channels. The physical meaning of such `confinement' is related to the non--trivial magnetic interaction of color currents in the quark--gluon plasma. Our results do not contradict the idea that the normal electric interaction of color charges is screened and produces no bound states in the usual sense.