Lagrangian formulation for arbitrary spin. II. The fermion case

The Rarita-Schwinger formalism for fermion fields is brought to a Lagrangian form in the case of arbitrary spin. The requirement that all differential equations of the field should follow from the variation of an action integral necessitates the introduction of additional fields in the theory. By demanding that these auxiliary variables vanish in the case of no interaction, an explicit form is obtained for the Lagrangian. The resulting theory is found to reproduce the usual formalism in the case of spin $\frac{3}{2}$, and turns out to be in agreement with results obtained by Chang for spin values $\frac{5}{2}$ and $\frac{7}{2}$. The Galilean limit of the minimally coupled equations yields the minimal Galilean-invariant theory of Hagen and Hurley. The $g$ factor turns out to be $\frac{1}{s}$, in accordance with a long-standing conjecture.