Lagrangian Formulation ofŨ(12)Symmetry and the Bargmann-Wigner Equations

The problem of finding Lagrangian functions which yield the Bargmann-Wigner equations is discussed, and is solved explicitly for the case of third-rank spinors. The formalism provides a field-theoretic realization of the $\tilde{U}\mathrm{}\left(12\right)\mathrm{}$ symmetry theory proposed by Salam, Delbourgo, and Strathdee. A general expression for the residue at the physical particle pole corresponding to an arbitrary multiplet is given, in a simple form which exhibits the symmetries of the theory. The propagators for the 143 and 364 representations are analyzed in detail.