Galilean covariant theories for Bargmann–Wigner fields with arbitrary spin

Abstract

We construct Lagrangians for non-relativistic massive fields with arbitrary spin. We use a Bargmann–Wigner construction, together with a Galilean covariant approach based on the reduction from an extended (4, 1) Minkowski manifold to the Galilean (3, 1) spacetime. Fierz identities are developed within this framework. By using symmetric spinor fields of rank 2 and rank 3, we can avoid the difficulty arising from the introduction of the minimal electromagnetic interaction in the Bargmann–Wigner wave equations. For fields with spin S, the minimal electromagnetic coupling thereby leads to the gyromagnetic ratio gS = 1/S.