HARD THERMAL LOOPS, STATIC RESPONSE, AND THE COMPOSITE EFFECTIVE ACTION

First, we investigate the static non-Abelian Kubo equation. We prove t hat it does not possess finite energy solutions; thereby we establish that gauge theories do not support hard thermal solitons. This general result is verified by a numerical solution of the equations. A simila r argument shows that ''static'' instantons are absent. In addition, w e note that the static equations reproduce the expected screening of t he non-Abelian electric field by a gauge-invariant Debye mass m = gT s quare-root (N + N(F)/2)/3. Second, we derive the non-Abelian Kubo equa tion from the composite effective action. This is achieved by showing that the requirement of stationarity of the composite effective action is equivalent, within a kinematical approximation scheme, to the cond ition of gauge invariance for the generating functional of hard therma l loops.