Lorentz Invariant Equations for Multiplets and Their Gauge

This paper explores the existence of kinematical gauge transformations for Lorentz invariant equations which describe a multiplet of two spin $\frac{1}{2}$ particles. For this multiplet the additional gauge invariance can be in form of three different groups of transformation. This gauge is absent when the particles are treated separately. Some basic properties of the solutions for these “multiplet equations” are analyzed.