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.

• Received 25 May 1955

DOI:https://doi.org/10.1103/PhysRev.100.924