Spacetime Quantization of BPFTW Action: Spacelike Plasmon Cut \& New   Phase of the Thermal Vacuum
  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 $T$. 
Ngee-Pong Chang