Abstract
Relativistic theory for the family of the principal meson trajectories was constructed. In the framework of relativistic quantum mechanics the coordinates of quarks should be noncommutative, which leads to a set of consistency conditions. Exploiting the geometrical basis of our model, we have obtained relativistic analogs of orbital and spin momenta and construct the gauge-invariant coordinates of physical particles. It makes possible to introduce the interaction terms in a simple geometrical way.
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