Here $\Gamma ^{\left( 2\right) }$ is the one-loop fermion contribution to the effective action in the linear approximation. The operators $\Pi _{\nu }$ and $\Pi _{\mu \nu }$ are calculated using the fermion thermal Green’s function in the presence of the background field $\overline{b}$ (2.17). They represent the fermion tadpole and one-loop polarization operators respectively. Their leading behaviors for static $\left( k_{0}=0\right) $ and slowly $\left( {\bf k}\sim 0\right) $ varying configurations in the frame ${\bf k}=(k,0)$ take the form

$$\Pi _{k}\left( x\right) =0,\;\;\;\Pi _{0}\left( x\right) =-n_{e},\;\;\;\Pi
_{\mu \nu }=\left( 
\begin{array}{ccc}
{\it \Pi }_{{\it 0}}+{\it \Pi }_{{\it 0}}\,^{\prime }\,k^{2} & 0 & {\it \Pi }%
_{{\it 1}}k \\ 
0 & 0 & 0 \\ 
-{\it \Pi }_{{\it 1}}k & 0 & {\it \Pi }_{\,{\it 2}}k^{2}
\end{array}
\right) ,  \eqnum{3.2}$$

The independent coefficients: ${\it \Pi }_{{\it 0}}$, ${\it \Pi }_{{\it 0}%
}\,^{\prime }$, ${\it \Pi }_{{\it 1}}$ and ${\it \Pi }_{\,{\it 2}}$ are functions of $k^{2}$, $\mu $ and $\overline{b}$. In order to find them we just need to calculate the $\Pi _{\mu \nu }$ Euclidean components: $\Pi
_{44} $, $\Pi _{42}$ and $\Pi _{22}$. In the Landau gauge these Euclidean components are given by[@11],

$$\Pi _{44}\left( k,\mu ,\overline{b}\right) =-\frac{1}{\beta }%
