Debye Screening , Kms and Imaginary - Time Formalism of Temporal Axial Gauge

We argue that in QCD, the Debye mass requires not only a mathematical definition but also a physical one and temporal axial gauge could provide for a physical screening potential for this purpose. Unfortunately, this gauge is spoiled by problem of energy conservation rather than the well known divergence due to the double pole in the longitudinal propagator. We also show that KMS condition is violated in this gauge and is therefore not universally true. Since the beginning of the nineties, it is known that at finite temperature, in order to do true perturbative calculations order by order in the coupling constant, it is necessary to perform Braaten-Pisarski resummation[1] and use effective propagators and vertices in place of the bare quantities. This resum-mation requires the hard thermal loops[2] of the N-point functions. These are essentially the leading terms of the one-loop N-point functions. In real-time, there is the doubling of the degrees of freedom, so in principle, one will have to work out all the components of each N-point hard thermal loops before one can do resummation. This is, however, not necessary in imaginary-time. There is only one hard thermal loop for each N-point function so imaginary-time is comparatively simple to work in. Furthermore, when considering static problem like calculating the Debye mass at the next to leading order,