  We present an exploratory numerical study on the lattice of the color
structure of the wave functionals of the SU(3) Yang-Mills theory in the
presence of a $q\bar q$ static pair. In a spatial box with periodic boundary
conditions we discuss the fact that all states contributing to the Feynman
propagation kernel are global color singlets. We confirm this numerically by
computing the correlations of gauge-fixed Polyakov lines with color-twisted
boundary conditions in the time direction. The values of the lowest energies in
the color singlet and octet external source sectors agree within statistical
errors, confirming that both channels contribute to the lowest (global singlet)
state of the Feynman kernel. We then study the case of homogeneous boundary
conditions in the time direction for which the gauge-fixing is not needed. In
this case the lowest energies extracted in the singlet external source sector
agree with those determined with periodic boundary conditions, while in the
octet sector the correlator is compatible with being null within our
statistical errors. Therefore consistently only the singlet external source
contribution has a non-vanishing overlap with the null-field wave functional.
