Quon Statistics for Composite Systems and a Limit on the Violation of the Pauli Principle for Nucleons and Quarks

The quon algebra gives a description of particles, “quons,” that are neither fermions nor bosons. The parameter q attached to a quon labels a smooth interpolation between bosons, for which q = +1, and fermions, for which q = −1. Wigner and Ehrenfest and Oppenheimer showed that a composite system of identical bosons and fermions is a fermion if it contains an odd number of fermions and is a boson otherwise. Here we generalize this result to composite systems of identical quons. We find qcomposite = qn 2 constituent for a system of n identical quons. This result reduces to the earlier result for bosons and fermions. Using this generalization we find bounds on possible violations of the Pauli exclusion principle for nucleons and quarks based on such bounds for nuclei. email address, [email protected]. email address, [email protected] The celebrated spin-statistics theorem [1] gives the spin-statistics connection that lies at the heart of the quantum mechanics of many-body systems: spin onehalf particles are fermions and integer spin particles are bosons. Wigner [2] and Ehrenfest and Oppenheimer [3] found the fundamental result that composite systems of identical bosons and fermions are bosons, unless they have an odd number of fermions, in which case they are fermions. Given the usual rules for addition of angular momenta, the Wigner–Oppenheimer-Ehrenfest (WEO) result extends the spin-statistics connection to composite systems. The WEO result requires that all the composites must be in the same internal quantum state and that the interactions between the composites must be sufficiently weak not to change the internal states of the composites. In this letter we generalize the WEO result to cases where the bound states are composed of identical particles that need not be either bosons or fermions. Recently one of us introduced a formalism, using the quon algebra, that can describe small violations of the usual spin-statistics connection [4]. In this formalism identical particles can occur in states associated with a mixture of different representations of the symmetric group, with the weights of the mixture dependent on a parameter q. To introduce the quon algebra, recall that bosons are described by the algebra of commutators of the creation and annihilation operators a(k)a†(l) − a†(l)a(k) = δ(k, l), (1) and fermions are described by the algebra of anticommutators of the creation and annihilation operators, a(k)a†(l) + a†(l)a(k) = δ(k, l). (2) The quon algebra is the convex sum of these two expressions, where Eq.(1) is multiplied by (1 + q)/2, Eq.(2) is multiplied by (1− q)/2, and the equations are added. For the sum to be convex q must be between −1 and 1. Several authors have shown that when q is in this range all the squared norms of states are positive. [5] Thus the quon algebra is a(k)a†(l) − qa†(l)a(k) = δ(k, l). (3)