3-FERMION RELATIVISTIC BOUND-STATES AND CLUSTER DECOMPOSITION

We write a system of N coupled compatible Dirac equations. The energy eigenvalue equation is obtained by simply adding the free Hamiltonians and the mutual interaction potentials. We write also a system of three coupled compatible Dirac equations, which is more complicated but completely separable (we obtain three free equations if we «switch off» the three mutual interactions, but we obtain also two coupled and one free equations if we «switch off» two of the three mutual interactions only). As an example, we present a three-fermion symmetric relativistic harmonic-oscillator model. © 1990 Società Italiana di Fisica.