Gauge groups and Noether’s theorem for continuum mechanics

The group of ’’gauge’’ transformations of variables which arise in the Hamiltonian formulation of dissipation‐free continuum systems is discussed. These transformations leave all physical quantities invariant. The quantities which are thereby conserved as a result of Noether’s theorem are discussed in the cases that the group is Abelian or non‐Abelian. Magnetohydrodynamics and stratified fluids are examples of these two cases.