Quantum Yang-Mills Charges in Strongly Coupled 2D Lattice QCD with Three Flavors

We investigate the quantum properties of the truly gauge-invariant and conserved charges of two-dimensional Yang-Mills theories, focusing on lattice QCD in the strong coupling regime. The construction of those charges uses the integral version of the (1+1)-dimensional Yang-Mills equations, and they correspond to the eigenvalues of a charge operator. The gauge invariance of the charges suggests that they are not confined, hence hadronic states may carry them. Using the Feynman-Kac formalism, we evaluate the correlation functions of those charges on baryon and meson states through functional integrals over the gauge group SU(N) (N=2,3) and Grassmannian variables - the fermionic fields. Our results show that the expectation values of the lowest non-trivial charges are nonzero for baryon and meson states but vanish for non-gauge-invariant states, supporting the interpretation that hadrons indeed carry these charges. While renormalization effects and higher-order contributions remain to be analyzed, these findings point toward a potential link between gauge-invariant charges and confinement.