with $\gamma = O(1)$. Adding static sources does not modify the parameters of the vacuum gluon distribution, [*e.g.*]{} $\omega(p)$. This is because the vacuum energy is an extensive quantity while sources contribute a finite amount to the total energy. Thus we can use the three functions $\omega$, $d$ and $f$ calculated in the absence of the sources to compute the expectation value of the chromo-electric field in the presence of static sources. The ansantz state obtained by applying quark sources to the variational vacuum of Eq. (\[varia\]) does not, however optimize the state with sources.

 The field lines in the $Q{\bar Q}$ and $QQQ$ systems 
------------------------------------------------------

For a quark and an antiquark at positions $\x_q \equiv \R/2 = 
  R{\hat \z}/2$ and $\x_{\bar q} = -\R/2 = -R{\hat \z}/2$, respectively, and the gluon field distributed according to $\Psi[\A]$, the expectation value of the square of the magnitude of the chromo-electric field measured at position $\x$ is given by

$$\begin{gathered}
\langle \E^2(\x,\R) \rangle   =  { \frac{C_F}{(4\pi)^2}}
  \sum_{\z_1=\pm \R/2} \sum_{\z_2 =\pm \R/2} \pm 
 \int d\y_1 d\y_2 \\
\times{  \frac{ (\x - \y_1)\cdot (\x-\y_2)}{|\x - \y_1|^3
 |\x - \y_2|^3}} E(\z_1,\y_1;\z_2,\y_2), \label{qq}\end{gathered}$$

where the $+ (-)$ sign is for the $\z_1 =(\ne) \z_2$ contributions, and 