(a) Show that Noether's theorem for global \(S U(3)_{\text {color }}\) symmetry in QCD leads to the conserved color current \(j_{\mu}^{a}=\bar{\psi}_{i} \gamma_{\mu} T_{i j}^{a} \psi_{j}-f^{a b c} A_{u}^{b} F_{\mu u}^{c}\) and hence that \(d Q^{a} / d t=0\) where \(Q^{a}=\int d^{3} x j_{0}^{a}\) in the usual way.

(b) Show that the quark component of the color current \(j_{q \mu}^{a} \equiv \bar{\psi}_{i} \gamma_{\mu} T_{i j}^{a} \psi_{j}\) satisfies \(D^{\mu b c} j_{q \mu}^{c}=\) 0 and hence that \(\partial^{\mu} j_{q \mu}^{a} eq 0\). Explain why QED-like Ward-Takahashi and Ward identities do not apply in QCD.