Barut equation for the particle-antiparticle system with a Dirac oscillator interaction

Barut showed us how it is possible to get a Poincaré invariant n-body equation with a single time. Starting from the Barut equation for n-free particles, we show how to generalize it when they interact through Dirac oscillators with different frequencies. We then particularize the problem to n=2 and consider the particle-antiparticle system whose frequencies are respectively and –. We indicate how the resulting equation can be solved by perturbation theory, though the spectrum and its comparison with that of the mesons will be given in another publication.Member of El Colegio Nacional and El Sistema Nacional de Investigadores.Fellow of El Sistema Nacional de Investigadores (México).