Perfect fluid coupled to a solenoidal field which enjoys the ℓ-conformal Galilei symmetry

Abstract

A non-relativistic (Galilei-invariant) model of a perfect fluid coupled to a solenoidal field in arbitrary spatial dimension is considered. It contains an arbitrary parameter κ and in the particular case of κ=1 it describes a perfect fluid coupled to a magnetic field. For a special value of κ, the theory admits the Schrödinger symmetry group which is consistent with the magnetic case in two spatial dimensions only. Generalization to the case of the ℓ-conformal Galilei group for an arbitrary half-integer parameter ℓ is constructed.