- 
 \theta(\mu - |\l|)\theta(\mu - |{\L\over 2}|) \right]  
 \sim f\left( {\p + \q}\over 2 \right) \theta(\mu - p) \theta( \mu - q) 
  + \left[ 1 - \theta(p) \theta(q) \right],  \label{f}$$

[*i.e.*]{} in the term in the bracket we ignore the short distance logarithmic corrections. It is easy to show that if logarithmic corrections are ignored then the short-range, $p,q > \mu$ contribution to the energy density is the same as in the Abelian case. Since we are mainly interested in the long range behavior of the chromo-electric field, in the following we shall ignore contributions from the region $p,q>\mu$ all together. In the long-range approximation, $x, R >> 1/\mu$ the expectation value of $\E^2$ is then given by,

$$\langle \E^2(\x,\R) \rangle = 
 {{C_F}\over {(4\pi)^2}}  
\sum_{ij=1}^2 \xi^{Q\bar Q}_{ij} \int d\r f_L(r) 
  {{\z_i - \x - \r/2} \over {|\z_i - \x - \r/2|}}
\cdot   {{\z_j - \x + \r/2} \over {|\z_j - \x + \r/2|}}  
 d'_L(\z_i - \x - \r/2) d'_L(\z_j - \x + \r/2).
  \label{el}$$

$\xi^{Q\bar Q}_{ij} = 1$ for $i=j$ and $-1$ for $i\ne j$, $\z_{1,(2)} = (-)\R/2$, $$d'_L(r) \equiv  {2\over {\pi}}\int^\mu_0 p dp j_1(rp) d(p), \label{dpl}$$ is the derivative of $d_L$ w.r.t. $r$, $$f_L(r) = {1\over {2\pi^2}} \int^\mu_0 dp 