R. Jackiw et al., HARD THERMAL LOOPS, STATIC RESPONSE, AND THE COMPOSITE EFFECTIVE ACTION, Physical review. D. Particles and fields, 49(12), 1994, pp. 6787-6793
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.