Divergence anomaly and Schwinger terms: Towards a consistent theory of anomalous classical fluids

Article Type

Research Article

Publication Title

Physical Review D


In this Letter, anomaly, which is a generic feature of relativistic quantum field theory (QFT), is shown to be present in non-relativistic classical ideal fluid. Also, in this model we have found the presence of anomalous terms in current algebra, an obvious analogue of Schwinger terms in QFT. We work in the Hamiltonian framework, where Eulerian dynamical variables obey an anomalous algebra (with Schwinger terms) that is inherited from modified Poisson brackets, with Berry curvature corrections, among Lagrangian discrete coordinates. The divergence anomaly appears in the Hamiltonian equations of motion. A generalized form of the fluid velocity field can be identified by the "anomalous velocity"of Bloch band electrons appearing in the quantum Hall effect in condensed matter physics. Finally, we show that the divergence anomaly and Schwinger terms satisfy the well-known Adler consistency condition, and we mention possible scenarios that can be impacted by this new anomalous fluid theory.



Publication Date



Open Access, Hybrid Gold

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