EXAMPLES OF PARASTATISTICS

The pairing model of nuclear physics for a single j shell is shown to define a para-Fermi statistics of order j + 1 2; the parafermion is a pair with total spin zero and is usually represented by the quasi-spin raising operator of Kerman. The description of a single spin 1 2 fermion in a 3-dimensional harmonic oscillator with spin-orbit force is next shown to define a para-Bose statistics of order 3; the paraboson is a quantum of excitation with total spin zero and is Joseph's self-adjoint ladder operator for the harmonic oscillator. In neither case do there exist Klein transformations which reduce the formalism to ordinary statistics. A model field theory of a cluster is discussed and shown to present strong analogies with parastatistics. A new structure ansatz complementing Green's ansatz for a parafield is given and used to establish the equivalence of Greenberg's paraquark model of the nucleon and Nambu's three-triplet model. It is suggested that paraquanta may represent composite" particles having an "intrinsic" form factor and nonlocal properties and as such might be better viewed as "elementary excitations" of the system. © 1969."