Consistency of Spin-One Theory

The energy eigenvalues of a generalized equation for the motion of the spin-1 particle in a homogeneous magnetic field are solved by using a very simple method. From the explicit expression of the eigenvalues, it is found that the spin-1 theory is consistent when the anomalous magnetic moment $\kappa \left(H^2\right)$ is a nonpolynomial function of the magnetic field strength $\mathrm{}\left|H\right|\mathrm{}$ that obeys certain conditions. Hence, the usual way of writing the spin-1 equation, with constant anomalous magnetic moment, is inconsistent. A particular form for $\kappa \left(H^2\right)$ which gives consistency for spin-1 theory is discussed. Some physical implications are also presented.