throughout the paper we use standard lattice notations and so the factors of the lattice spacings are implicit and all fields are dimensionless.

The quantum fields that describe quarks are the fermion fields $\psi^{a\alpha}_{x}$ that live on the sites $x$ of the lattice. They have color indices $a=1,\dots,N$, and Dirac indices $\alpha=1,2$ (again, recall we are in $1+1$ dimensions). The Fermi fields obey the following anti-commutation relations $$\left\{ \psi^{a\alpha}_x,\psi^{\dag b \beta}_y \right\} = \delta_{xy}\delta_{ab}\delta_{\alpha\beta}. \label{anticomm}$$

Choosing to work in the temporal gauge that fixes $A_0=0$ removes one degree of freedom (and its conjugate momentum). This leaves the spatial gauge field operators $\left(U_x\right)_{ab}$ living on the lattice link between $x$ and $x+1$. For definiteness we note that the operator $\left(U^\dag_{x}\right)_{ab}$ is [*defined*]{} to be equal to $\left(\left(U_{x}\right)_{ba}\right)^\dag$, and so the following holds as a operator identity $$\sum_a\, \left(\left(U_{x}\right)_{ab}\right)^\dag\, \left(U_{x}\right)_{ac} = \sum_a\, \left(U^\dag_{x}\right)_{ba}\, \left(U_{x}\right)_{ac}=\delta_{bc}.$$ The conjugate momenta of the $U$’s also reside on links and are denoted by $E^i_{x}$, $i=1,\dots,N^2-1$. The following are the commutation relations of this set of operators, $$\begin{aligned}
\left[ E^i_{x} , \left( U_{x} \right)_{ab} \right] &=& \left( \lambda^i U_{x} \right)_{ab}, \label{comm_plus1} \\
\left[ E^i_{x} , E^j_{x} \right] &=& i f^{ijk} E^k_{x}. \label{comm_plus2}\end{aligned}$$ Here $\lambda^i$ are matrices that represent 