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$SO(N)$ symmetric theory of $N$ real scalar fields, why do charges have correct commutation relations of generators?

Consider an $SO(N)$ symmetric theory of $N$ real scalar fields,$$\mathcal{L} = {1\over2} \partial_\mu \Phi^a \partial^\mu \Phi^a - {1\over2} m^2 \Phi^a \Phi^a - {1\over4} \lambda(\Phi^a \Phi^a)^2.$$For the quantum theory, consider the $SO(N)$ charges $\hat{Q}_{ab} = \int d^3 \textbf{x}\,\hat{J}_{ab}^0$. Why do the charges $\hat{Q}_{ab}$ have correct commutation relations of the generators of the $SO(N)$ symmetry?