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Anomaly, a generic feature of relativistic quantum field theory, is shown tobe present in non-relativistic classical ideal fluid. A new result is thepresence of anomalous terms in current algebra, an obvious analogue ofSchwinger terms present in quantum field theory. We work in Hamiltonianframework where Eulerian dynamical variables obey an anomalous algebra (withSchwinger terms) that is inherited from modified Poisson brackets, with Berrycurvature corrections, among Lagrangian discrete coordinates. The divergenceanomaly appears in the Hamiltonian equations of motion. A generalized form offluid velocity field can be identified with the "anomalous velocity" of Blochband electrons appearing in quantum Hall effect in condensed matter physics. Wefinally show that the divergence anomaly and Schwinger terms satisfy well knownAdler consistency condition. Lastly we mention possible scenarios where thisnew anomalous fluid theory can impact.

Divergence Anomaly and Schwinger Terms: Towards a Consistent Theory of Anomalous Classical Fluid