Hamilton Principle for Chiral Anomalies in Hydrodynamics

TL;DR

This paper develops a covariant Hamilton framework for chiral hydrodynamics with axial-vector potentials, revealing how quantum anomalies manifest in classical fluid flows with helicity and chiral imbalance.

Contribution

It introduces a Hamilton principle-based approach to incorporate axial potentials into hydrodynamics, deriving anomaly expressions and extending Euler equations for chiral flows.

Findings

Derived hydrodynamic expressions for vector and axial currents.

Extended Euler equations to include axial potential effects.

Revealed the kinematic origin of quantum anomalies in classical hydrodynamics.

Abstract

We developed the spacetime-covariant Hamilton principle for barotropic flows of a perfect fluid in the external axial-vector potential conjugate to the helicity current. Such flows carry helicity, a chiral imbalance, controlled by the axial potential. The interest in such a setting is motivated by the recent observation that the axial-current anomaly of quantum field theories with Dirac fermions appears as a kinematic property of classical hydrodynamics. Especially interesting effects occur under the simultaneous actions of the electromagnetic field and the axial-vector potential. With the help of the Hamilton principle, we obtain the extension of the Euler equations by the axial potential and derive anomalies in the divergence of the axial and vector current. Our approach provides a hydrodynamic expression for vector and axial currents and lays down a platform for studying flows with a chiral imbalance and their anomalies.