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 κ(H²) is a nonpolynomial function of the magnetic field strength $|H|$ 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 κ(H²) which gives consistency for spin-1 theory is discussed. Some physical implications are also presented.