Barut equation for the particle-antiparticle system with a Dirac oscillator interaction
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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 ω and −ω. 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.
KeywordsPerturbation Theory Single Time Dirac Oscillator Oscillator Interaction
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