Anomalous hydrodynamics is a low-energy effective theory that captures anomaly-induced transport such as the chiral magnetic effect. Although there are several derivations of anomalous hydrodynamic equation from microscopic quantum theory, it has been unclear how we can derive it based on the operator formalism of quantum theory. In this study, we derive anomalous hydrodynamic equation based on so-called Mori's projection operator method, which provides a systematic way to derive the equation of motion for slow variables like conserved charge densities in hydrodynamics. The vital point for Mori's projection operator method is that it gives a generalization of the current algebra technique used in low-energy hadron dynamics of the QCD vacuum to the nonequilibrium situations. As a result, we find that the chiral magnetic effect is caused by the anomalous commutation relation between vector and axial charge densities which represents a manifestation of the quantum anomaly in the operator formalism. We further discuss an extension of our derivation to the symmetry-broken phase which brings about anomalous superfluid hydrodynamics.
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