Gauge Symmetries and Noether Charges in Clebsch-Parameterized Magnetohydrodynamics

TL;DR

This paper demonstrates how Clebsch parameterization transforms Casimir invariants into Noether charges related to gauge symmetries in ideal fluid and plasma dynamics, specifically in magnetohydrodynamics.

Contribution

It explicitly identifies the gauge symmetries of Clebsch parameterization and shows their relation to conserved quantities in magnetohydrodynamics.

Findings

Casimir invariants become Noether charges under parameterization

Explicit forms of gauge symmetries are derived

Connection between gauge symmetries and conserved quantities established

Abstract

It is shown that the Clebsch parameterization, upon canonizing the Hamiltonian system of ideal fluid or plasma dynamics, converts the Casimir invariants (mass and helicities) in the original noncanonical formulation into the Noether charges pertinent to the gauge symmetries of the parameterization. The problem is addressed in the context of magnetohydrodynamics. The concrete forms of the gauge symmetries of Clebsch parameterization are worked out.