A New Diffeomorphism Symmetry Group of Magnetohydrodynamics

Abstract

Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. Yahalom (A four function variational principle for Barotropic magnetohydrodynamics, EPL 89, 34005 (2010) has shown that barotropic magnetohydrodynamics is mathematically equivalent to a four function field theory defined a by a Lagrangian for some topologies. The four functions include two surfaces whose intersections consist the magnetic field lines, the part of the velocity field not defined by the comoving magnetic field and the density. This Lagrangian admits a newly discovered group of Diffeomorphism Symmetry. I discuss the symmetry group and derive the related Noether current.