Internal Structure of Spinning Particles

Elementary particle models with internal degrees of freedom have been investigated within the framework of special relativity and orthodox quantum mechanics. Classical arguments indicate that systems whose extensions are ≲ their Compton wavelength have spin excitation energies ≳ their rest mass. The principal aim of this paper is enumeration and classification of particles with rigid internal structure and a useful classification of particle models is by their symmetry groups. In nonrelativistic mechanics this classification shows that there are only the three well-known types of rigid systems that might be labeled by number of degrees of freedom as [0], [2], and [3] and are exemplified by an ideal point, diatomic molecule and rotator, respectively; while of the three types, but one, [3], possesses a spin-½ state of the Pauli-electron type. The corresponding analysis for relativistic mechanics shows there are nine types labeled here [0], [2], [3], [3′], [4], [4′], [4″], [5], and [6], and in addition two one-parameter infinities of types [$3_f$] and [$5_f$] ($0\le f\le \pi$). An algorithm exists for obtaining the spin-spectra of rigid structures from their symmetry groups. Of the $9+2\infty$ types, just three ([4], [5], and [6]) possess spin-½ states of the Dirac-electron type. The apparent rest mass depends upon the internal rotational state of the particle, as is shown by an unrealistic example of a Lagrangian which is an extension of that of the Klein-Gordon particle.