Properties of Half-Integral Spin Dirac-Fierz-Pauli Particles

A method is developed to eliminate extraneous components from the Dirac-Fierz-Pauli equations for half-integral spin particles. Starting from the Rarita-Schwinger formulation, Hamiltonian forms of the equations for the independent components of the wave functions are obtained. The process is carried out in detail for the field-free spin $\frac{3}{2}$ and spin $\frac{5}{2}$ particles and the reduced equations are quantized. It is shown that the interaction with the electromagnetic field can be introduced in an infinite variety of ways. A one-parameter class of equations containing the interaction is obtained for each spin. By reducing these equations in the nonrelativistic limit it is shown that the gyromagnetic ratio is in each case independent of the parameter and has the unique value of the reciprocal of the spin. For the cases of spin $\frac{3}{2}$ and spin $\frac{5}{2}$, the quadrupole moment is also obtained. It has the unique value $+\left(\frac{5}{3}\right){\left(\frac{\hslash }{\mathrm{mc}}\right)}^2$ for spin $\frac{3}{2}$. For spin $\frac{5}{2}$, it depends on the parameter but is close to $+\left(\frac{28}{15}\right){\left(\frac{\hslash }{\mathrm{mc}}\right)}^2$ over most of its range.