Motion of spin-1 particles in a homogeneous magnetic field: multispinor formalism

A general method of calculation within the multispinor formalism is proposed. It is then used to calculate the eigenvalues of the theory of particles with any spin moving in a homogeneous magnetic field, without explicitly solving the equation of motion. The spin-1 theory with anomalous-magnetic-moment couplings is examined specifically. The results differ from those obtained by Tsai and Yildiz using the vector theory, and from those obtained by Goldman and Tsai and by Krase, Lu, and Good using the six-component theory. It is found that the discrepancies are due to the fact that different nonminimal couplings are in fact added to various theories. However, when only minimal couplings are considered, all three theories predict the same eigenvalues. In this case, the square of an eigenvalue is a perfect square and is positive definite. In the case where nonminimal couplings are added, the square of an eigenvalue can become negative in all three theories, i.e., the energy eigenvalues can become pure imaginary. Possible physical interpretations of the results are discussed.