Relativistic harmonic oscillator for spin-1/2 particles in the Bethe-Salpeter formalism

A kernel for the spin-1/2 relativistic Bethe-Salpeter equation is proposed and the equation is solved in the nonrelativistic limit for the mass spectrum in the case of vector coupling. Numerical results are also presented for the fully relativistic case. It is found that in addition to the ordinary, evenly spaced energy levels of the nonrelativistic harmonic oscillator, the spin coupling produces another family of states with level spacing proportional to n, the principal quantum number. It is also found that in this model the phenomenology of the mesons can be reproduced qualitatively only for couplings strong enough to produce significant relativistic effects in the lowest-lying levels