field $E$ by $|0\>_G$, $$E^i| 0 \>_G = 0, \qquad \forall i.$$ Any application of the link operators $\left( U_{x} \right)_{ab}$ on $|0\>_G$, creates states which correspond to flux lines on the link $x$. The state $|0 \>_G$ is the only state with no flux at all. Using the fact that the electric field operators generate a $SU(N)$ algebra, one can distinguish between the different quantum states created by the link operators as follows. Define the quadratic Casimir operator $$\vec{E}^2_{x}\equiv\sum_{i=1}^{N^2-1}E^{i2}_{x}. \label{E2}$$ It is clear that the flux-less state $| 0 \>_G$ is an eigenstate of this Casimir, with zero eigenvalue. Next, the commutations of the Casimir with the link operators are verified from to be $$\left[ \vec{E}^2_{x},\left( U_{x} \right)_{ab} \right] = C_F\left( U_{x} \right)_{ab},$$ where $C_F=(N^2-1)/2N$ is the Casimir operator in the fundamental representation. This means that the state $\left[ \left( U_{x} \right)_{ab}| 0 \>_G \right]$ is also an eigenstate of (\[E2\]), with eigenvalue equal to $C_F$. One can now classify the states in $|\Omega \>_G$ according to their $\vec{E}^2$ eigenvalue. The result is a Hilbert space with a ladder-like structure. The lowest state is $|0\>_G$, with zero flux, and is a singlet of $SU(N)$. Repeated applications of the gauge 