Lagrange formulation of the symmetric theory of massive spin-3 fields

Abstract

The description of massive spin-3 fields by the Lagrangian formulation based on the symmetric tensor field of rank 3 requires auxiliary fields in order to derive all of the subsidiary conditions. We construct the Lagrangian formulation of the symmetric theory of massive spin-3 fields by introducing the auxiliary field belonging to the representation $D(\frac{1}{2},\frac{1}{2})$ of the proper orthochronous Lorentz group. A linearized Lagrange function is also proposed in order that electromagnetic interactions can be introduced in an unambiguous fashion. The canonical commutation relations are obtained by using the action principle. The Green's function is derived from the Schwinger formulation.