  In this paper, we perform the quantization of the nonlocal BPFTW effective
action in coordinate space. The action is made local by using a conjugate set
of auxiliary fields. The action summarizes the properties of quark propagation
through a hot environ. The fermion propagator shows a pseudo-Lorentz invariant
particle pole as well as a pair of conjugate spacelike plasmon cut. We relate
the cuts to the homogeneous solutions of the local equations of motion for
auxiliary fields. Our quantization shows how the spacelike cut produces a
$90^{o}$ phase factor in the thermal vacuum at high $T$. This phase factor is
responsible for the vanishing of $ \psibarpsi $ at high $T$.
