Space-Time Model of Relativistic Extended Particles in Minkowski Space. II. Free Particle and Interaction Theory

Abstract

In this paper, we examine new consequences of the idea that particles are extended structures in real space-time. Starting from the general quantum equations for stable states established in paper I, we discuss the general form of solutions satisfying simultaneously the internal state equations and the external wave equations. One sees in particular that the external part depending on the particle's position $x_{\mu }$ necessarily corresponds to state vectors belonging to irreducible finite-dimensional representations of the Lorentz group ${\mathcal{L}}_4$. Assuming then that the general interaction Hamiltonians are invariant under ${\mathcal{L}}_4$ and our new internal isobaric spin group $G$, one justifies the usual semiempirical scheme of strong interactions (invariant under $S{O}_3$) and introduce weak interactions in isobaric spin space. The theory also implies couplings between external and internal motions and breaks automatically the symmetries of strong interactions, in a natural development of Sakurai's ideas.