Quantum Yang-Mills charges in strongly coupled <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mn>2</mml:mn> <mml:mi>D</mml:mi> </mml:math> 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 ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>1</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:mrow> </a:math> )-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 path integral formalism with imaginary time (Euclidean), we evaluate the correlation functions of those charges on baryon and meson states through functional integrals over the gauge group <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>S</c:mi> <c:mi>U</c:mi> <c:mo stretchy="false">(</c:mo> <c:mi>N</c:mi> <c:mo stretchy="false">)</c:mo> </c:math> ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>N</g:mi> <g:mo>=</g:mo> <g:mn>2</g:mn> </g:math> , 3) and Grassmannian variables—the fermionic fields. Our results show that the expectation values of the lowest nontrivial 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.