An Extended Relativistic Particle Model with Arbitrary Spin and Isospin

We consider a finite-dimensional Poincaré-invariant dynamical system with an additional $SU(2)$ symmetry that can be interpreted as a finite extended object evolving in Minkowski space. We show that for any value of the spin $s$, the mass spectrum $\{M\}$ of the system is determined by roots of the equation $Az_-^2+Bz_-+C+Dz_+=0$ where $z_{\pm}=a{M}^2\pm b\sqrt{s(s+1)}$ and the coefficients depend only on the state of “internal” variables. We discuss the possibility of describing certain meson and baryon states in terms of the model constructed.