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Poincare-invariant equations with a rising mass spectrum

Wilhelm I. Fushchych
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Abstract

In this note we shall construct, in the framework of relativistic quantum mechanics, the Poincare-invariant motion equations with realistic mass spectra. These equations describe a system with mass spectra of the form $m^2=a^2+b^2 s(s+1)$, where a and b are arbitrary parameters. Such equations are obtained by a reduction of the motion equation for two particles to a one-particle equation which describes the particle in various mass and spin states. It we impose a certain condition on the wave function of the derived equation, such an equation describes the free motion of a fixed-mass particle with arbitrary (but fixed) spin s.

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Wilhelm I. Fushchych. 2002-06-21. Poincare-invariant equations with a rising mass spectrum. https://arxiv.org/abs/quant-ph/0206156

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