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  • Letter
  • Open Access

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

Arpan Krishna Mitra1,* and Subir Ghosh2,†

  • 1Harish Chandra Research Institute, HBNI, Chhatnag Road, Jhusi, Uttar Pradesh 211019, India
  • 2Indian Statistical Institute, 203, Barrackpore Trunk Road, Kolkata 700108, India

  • *arpankrishnamitra@hri.res.in
  • †subir_ghosh2@rediffmail.com
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Phys. Rev. D 106, L041702 – Published 22 August, 2022

DOI: https://doi.org/10.1103/PhysRevD.106.L041702

Abstract

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.

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Phys. Rev. D 106, L041702– Published 22 August, 2022
  • Received 24 November 2021
  • Accepted 20 July 2022
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