Noether Theorem of Relativistic-Electromagnetic Ideal Hydrodynamics

TL;DR

This paper develops a variational framework for relativistic electromagnetic hydrodynamics, linking fluid momentum to Noether's theorem, and reproduces standard electromagnetic hydrodynamics with conserved fluid inertia.

Contribution

It introduces a novel variational approach that connects fluid momentum with conserved quantities via Noether's theorem in relativistic electromagnetic hydrodynamics.

Findings

The formulation reproduces standard electromagnetic hydrodynamics.

Fluid momentum is identified as a conserved quantity from Noether's theorem.

The approach ensures conservation of fluid inertia.

Abstract

We present a variational approach for relativistic ideal hydrodynamics interacting with electromagnetic fields. The momentum of fluid is introduced as the canonical conjugate variable of the position of a fluid element, which coincides with the conserved quantity derived from the Noether theorem. We further show that our formulation can reproduce the usual electromagnetic hydrodynamics which is obtained so as to satisfy the conservation of the inertia of fluid motion.