has been observed in the chromo-electric field in Ref. [@sho] and the “Y”-shape interaction advocated in Ref. [@kuzsim]. A recent reevaluation of the center-vortex model also supports the “Y”-shape [@corn].

In the following section we summarize the relevant elements of the Coulomb gauge formalism and discuss the approximations used. This is followed by numerical results and outlook of future studies. There is a fundamental difference between lattice gauge flux tubes corresponding to the distribution for the action density and the chromo-electric field profiles. In the context of the potential energy of the sources, this difference was emphasized in Zwanziger, Greensite and Olejnik [@goz; @zwancon]. We discuss those in Section. IV.

Chromo-electric Coulomb field in the presence of static charges
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The Coulomb gauge Hamiltonian
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The Yang-Mills Coulomb gauge Hamiltonian in the Schrödinger representation, $H=H(\Pi, A)$ is given by $$H  =  \frac{1}{2} \int d\x \left[ \bm{\Pi}^a(\x) \cdot \bm{\Pi}^a(\x) 
 +    \B^a(\x)\cdot \B^a(\x) \right] + {\hat V}_C. \label{h}$$ The gluon field satisfies the Coulomb gauge condition, $\na \cdot \A^a(\x)=0$, for all color components $a=1\cdots N_c^2-1$. The conjugate momenta, $\bm{\Pi}^a(\x)=  
   -i\partial/\partial {\A^a(\x)}$ obey the canonical commutation relation, $[\Pi^{i,a}(\x), A^{j,b}(\y)] = -i\delta_{ab} 
  \delta^{ij}_T(\na_\x)\delta(\x-\y)$, with $\delta^{ij}_T(\na) =
 \delta_{ij} - \nabla_i \nabla_i/\na^2$. The canonical momenta also 