Consider an operator (mathbf{U}=e^{i theta mathbf{G}}) with generator (mathbf{G}). If (mathbf{U}) commutes with a Hamiltonian (mathbf{H}), use

Question:

Consider an operator $\mathbf{U}=e^{i \theta \mathbf{G}}$ with generator $\mathbf{G}$. If $\mathbf{U}$ commutes with a Hamiltonian $\mathbf{H}$, use the first-order method to show that $\mathbf{G}$ also commutes with $\mathbf{H}$. What does this imply about $\mathbf{G}$ ?

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