Particle spectrum and geometrical symmetry

Abstract

The spectrum of unstable particles is studied on a model meeting the requirement of geometrical symmetry expressed by the restricted Lorentz groupL _r, which is represented by an unstable model particle described by the invariant tensor or spintensor of the groupL _r satisfying the Klein-Gordon equation. The problem of the spectrum of model particles is formulated and treated as a certain eigenvalue problem invariant with regard toL _r. The calculated spectrum of the reduced levels mass/width of the model particles is spin independent, agrees with the observed spectrum of resonances and shows that the model employed represents certain laws manifesting themselves in the observed spectrum of unstable particles.