Hydrodynamics with gauge anomaly: Variational principle and Hamiltonian formulation

TL;DR

This paper develops a variational and Hamiltonian framework for relativistic hydrodynamics incorporating gauge anomalies, providing a systematic approach to include gauge fields and anomalies in fluid dynamics.

Contribution

It introduces a variational principle and Hamiltonian formulation for anomalous relativistic hydrodynamics using Clebsch parametrization.

Findings

Derived equations of motion involving density and velocity fields.

Established the canonical framework and symmetry generators.

Analyzed the dependence of generators on Clebsch potentials with time-dependent backgrounds.

Abstract

We present a variational principle for relativistic hydrodynamics with gauge-anomaly terms for a fluid coupled to an Abelian background gauge field. For this we utilize the Clebsch parametrization of the velocity field. We also set up the Hamiltonian formulation and the canonical framework for the theory. While the equations of motion only involve the density and velocity fields, i.e., the Clebsch potentials only appear in the combination which is the velocity field, the generators of symmetry transformations (including the Hamiltonian) depend explicitly on one of the Clebsch potentials, if the background field is time-dependent. For the special case of time-independent background fields, this feature is absent.