Generalized Statistics and the Quark Model

Abstract

It is suggested that all symmetries in particle physics are either dynamical, and connected with Poincare invariance, or statistical, and connected with invariance under interchange of similar particles. To sustain this view, it is necessary to admit quantum statistics more general than Fermi or Bose statistics. Two different generalizations are considered: parastatistics and a new generalization called modular statistics. A discussion is developed of difficulties which arise with parastatistics of order three or more, but are resolved with the help of the corresponding modular statistics. Applications to the Nagoya model, the standard quark model and 'coloured' quark models are described, together with a dynamical model in which the quarks are identified with different kinds of tachyons.