Extension of Dirac theory and the classification of elementary particles

Abstract

The Dirac theory implies the existence of an internal vector space, in addition to spin space. Using Dirac's coupling of variables in internal space to those in physical space, we construct a new configuration structure for particles in the combined physical plus internal spaces. The importance of this is that the internal degrees of freedom implicit in Dirac's theory allow a new classification of elementary particles. An important consequence is the prediction of a new type of quark. As expected, our theory groups fermions into doublets, which are then divided into color singlets (leptons) and color triplets (quarks), and which are then further divided into generation singlets and generation triplets. If the Pauli exclusion principle for fermions is also valid within a particle's internal space, then our theory makes two important predictions. First, we can explain why the widely studied quarks (up, down, charm, strange, top, bottom) cannot be observed as free states in nature. Second, we predict the existence of a new quark which can indeed be observed as a free state in nature, and whose wave function is antisymmetric in internal space. W. M. Fairbank, a Guggenheim Fellow, has published experimental data which supports our second prediction.